Plenty of Good suggestions so far, but my personal list is rather "extensive" so I will probably be repeating a few things...
Effects: I don't think sounds are half as important as proper rendering. I want to see a dynamic solar and planetary system. The game will not support the making of a mine field out of asteroids, planetary defense grid, or "alternative" building methodologies (construction of underground habitats) if the graphics remain entirely 2d.
Improved AI. This is a definite must have. The AI continues to ignore certain staples in long term games. Certain AI's will not research Xeno Farms in 500 turns... If your civilization lacks the ability to build commercial farms after 10 years of growth 300 years in the future, then I think your species deserves to die off.
Remove Random Events! Every random event in the game is either better emulated as a guaranteed scenario event, a survey event, or as a result of player/PC choices. Jagged Alliance is BULLCRAP! The "best counter espionage structure in the galaxy" is no stop to this? Exactly 1/3? A galactic super power ripped asunder in a week? Nonsense! Dread lords return? Scenario event. Area (from planetary to large chunk of galaxy) changed environmentally includes population growth (could be nanites, could be energy, could be mutation virus, doesn't matter), planetary quality (ibid), research benefits, etc are all properly Survey Events (Your survey ship has located a "Blank" on this asteroid, planet, nebula, etc). Rampant piracy is either a scenario condition or something produced via espionage. Assassination of a public official is an espionage event or the result of sending an envoy to a planet with a high crime rate. Plague? I cannot articulate how stupid the computer is about plague. If your population is decimated to next to nothing, and someone offers you plague cure you take it right? Wouldn't the remaining population revolt if you refused whatever price? Plague is a bad idea for a galactic scale event anyway. Just how the heck did it get everywhere? No, plague is best suited as espionage or invasion consequences (occassionally a random survey event or ethical challenge).
Game Mantra: Micromanagement should be optimal (if done correctly) but not necessary. I should not have to micromanage my planetary crime rates, but if I desire to do so it should be mildly beneficial to do so.
Technology:
Organize the Tech Trees so that we will ALWAYS know where a given tech will appear. The "ethics" related techs are the biggest culprit for this one. Group related techs together.
No more unique techs! There are only pre-requisites. The reason why no one else can do something is because they are not able to live in aquatic ecology or because they lack the "glorious history tech." Tech points versus Advancement points (New Feature). Tech points allow you to research benefits within the current "paradigm" that you have. So if your race has "Quantum Religiosity" you are then able to develop the previously "Torian only" tech of Combat Trances (union between pilot and ship allows for better responses). Another Example: Certain ecologies will have easier access to certain techs or "equivalents." An artificial lifeform that developed on a volcanic world might be able to get "artificial sensibilities" (permanent 75% morale and 50% happiness regardless of factors) Note: Morale adds to soldiering so "Courage" becomes a superfluous stat and Heat tolerance (+5 soldiering versus foes armed with beam weapons) all right from the start. Basic research will get you access to small benefits that are within your current capability (increase structure/ship quality, advanced government benefits, small weapons bonus to current weapon systems (Lasers for instance), small bonus to current defense, Soldiering (this will have to be broken down into security, personal defense, and assault/invasion lines), etc. Whereas the "Big Techs" are the ones that define what you can do. Xeno Economics is the advent of pan-solar market systems. This grants a substantial bonus to economics. Xeno banking is just a derivative application of Xeno Economics and therefore is simply a "tech point" research under the "Xeno Economics Paradigm". A new paradigm for the economics line might be "Pan-Galactic Economic Direction" (With the advent of UltraComputers or Super Hive Mind or whatever... we are now able to unify economic thinking and application etc etc).
Ability to "research" new politcal party, religion, government model, etc. Why can't I switch back to dictatorship? Where are the other "governments?" Right now my civilization stands on the brink of annihilation: I am going to adopt a "War Party" stance and take their benefits. The other choice is extermination. I think most people would agree that a change in ideology is preferential to permanent extermination. The cost being tech points. To make the game even more "in depth" without wandering through the mire of "governmental models" simply use "Basic Governmenance" "Xeno Governance" "Galactic Governance" as paradigms and then allow "advanced" political parties to be "researched." So my "War Party" becomes "Xeno War Party" (as an example).
Civilization:
Borders should matter. Inside my galactic influence one should start having support problems (kind of like the isolationist super power, but can be expanded upon) since I am presumably using up resources and are going to have to "contend" with my "defenses" I have setup to defend my territory.
Diplomacy should be expanded (I should have all the options the computer does). The computer should not be DUMB about diplomatic options. If I offer to give you stuff that is valued at 3 times the total value of your entire empire put together for your one economic starbase there is precisely, ZERO reason why the computer should not be doing virtual jumping jacks to make that deal. Faction/Reputation should be expanded; saving someone's butt by giving them ships right at the brink of disaster usuallys makes people like you a LOT. Identifying a spy should identify which faction they are from (and the computer if they keep catching you should probably start to dislike you). Tourism should be faction specific as well; if a given people really like you, then they should probably be more likely to be a tourist on your worlds. War should make trade values change (blockade...) and drop tourism for those factions. Racial similarity in more than just ethics should also have faction consequences (mutually aquatic races for instance); sometimes good, sometimes bad. Alter the United Planets so that measures that get put to vote have reason to be there (I.E. some player/PC put the motion through). Dictatorships always get the "full" votes of their colonies, but the colonies are less influential due to the tight restrictions on them. The more "advanced" governments should grant greater planetary influence as well as economy.
Some of the ethical challenges are nonsense and the challenges need to be better balanced. In what galaxy is it immoral to save your people and presumably other species as well from the genetically engineered killing machine left behind by a long extinct race? I forget is stopping wanton genocide by murdering super beast a good or evil thing? Why are neutral options sometimes far more penalizing than good ones (using the current system)? In a more balanced system why would the evil option always be the most beneficial. There isn't even a reputation bonus for choosing good options. Most races should find it pleasing to note that you are not in the habit of exterminating species (reputation for mercy). But if you are in the habit of using mass drivers (reputation for being an evil bastard), then other races may choose to blockade your trade ships or something. There should be give and take; a -40% planetary production penalty should NOT be the only way to become significantly more good as a civlization. The planet is now more vulnerable to alien attack... How is this a good thing?
Planetary and Civilization morality should fluctuate. If planetary loyalty and/or happiness is low, then they should be more likely to stray from your government/cultural ethicality. If the preponderance of your worlds start adopting an ethical stance differenct from your own they will become more likely to revolt and your civilization will lose reputation with other races.
Space & Planets:
Tiles should ALWAYS be relevant. Most races CANNOT make use of a 300% food tile at all, and the 100% food tile is not always beneficial for a planet (low quality planets cannot get enough morale to want the greater population). Also certain structures might make other tiles unusable or decrease planetary quality (very large sized or very resource intensive structures) thus increasing the value of planetary quality.
More planetary statistics: Happiness (New Feature) and Morale (happiness determines how likely populous is to vote your way including passing legislation versus Morale that determines population growth and adds a small bonus to planetary production, research, economy, trade, planetary defense, etc... basically anything that high motivation can do). Crime, loyalty, espionage, etc should matter. High crime rates might decrease espionage resistance (but VERY high crime rates might mean increased epsionage resistance since chaos or mob rule can be hard to sabotage...) High loyalty should obviously affect how easily sabotage is accomplished but should also affect planetary stability (low ratings increase crime significantly). Espionage should be able to be used in a targeted manner: Sabotage (destroys build up or halts development of a square), Technology theft, diplomatic interference (assination), tactical advantage from stealing war secrets (bonus to planetary invasion or fleet combat), or Dissent (attack the loyalty, happiness, and ethics of planetary population). Depending on the action taken epsionage will be more or less hard to detect (agents will not automatically be detected unless a tech or structure is involved). Security (New Feature) acts as direct counter to espionage (high security ratings prompt happiness and planetary defense bonuses). Structure Quality (New Feature) increases the total output, building, and maintenance costs for all structures (should be small amount and vary slightly with technology: 1-20%).
Now that more statistics are relevant we can add an "additional" planetary focus. Military (increases military production, soldiering, and security), Research (increases research rate and total "advancement point" accrual), Commercial (increases food & social production as well as trade and small benefit to economy), Civil (increases loyalty, happiness, population growth, decreases crime, and grants small increase to benefits derived from political party).
Make Food matter. This is easily done by giving non-monetary costs to structures and penalties. Building Leisure sectors may increase happiness but also increase crime rate. Make most sectors have food costs in order to build/maintain. Industrial sectors might have low food costs (increase production), whereas commercial sectors (increase trade and economy) should have a large food cost. This also means that food trade/exportation between planets can matter and freighters will now actually "need" to be produced. Colonies should Not produce food they should require food. The larger the colony the more food that should be required in order to maintain it.
Planetary quality, Planet Size, and Environmental type should matter. High planetary quality might increase happiness but decrease overall soldiering (low survivability tends to make for hardcore soldiers) Noting: This would mean soldiers would have different soldiering values depending on which planet they are from Environmental types (toxic, radioactive, gaseous, aquatic, volcanic, organic (earth-like), barren, and artificial) and Planetary size (low gravity, normal gravity, and heavy gravity) should be used to determine planetary quality for your race (a machine race might do just fine on an artificial world without any additional research needed, whereas a racial swarm might do quite well on a gaseous world). Planetary quality will be determined by racial ecology. Terraforming will adapt a planet to your race's ecology thus increasing it for you but ensuring that the planet is less usable for other races with differing ecological needs. And Terraforming should have an ultimate limit based on planet size (obviously affected by technology allowing utilization of underground, underwater, etc, but still ultimately limited by planet size). The rate of terraforming should not be the result of social production. It should be a gradual process affected by certain technologies and structures (weather manipulation; biosphere manipulator sort of thing) that occurs over many weeks/months. Permanent damage to planetary quality is now MUCH harder to do. Damage the biosphere can be fixed with terraforming; it will just take a while. Only something which "forever" alters or removes chunks of the whole planet should do permanent damage. Core Detonation and Anti-matter bombardment come to mind. And if a planetary quality drops to 0 the planet is destroyed.
Let me make use of other planets and moons for resources. Advantages in space manipulation/exploitation can create heavy swings in survivability especially with a varied and wonderful space to utilize. Mining is altogether too cut and dry in this game. Let me mine nebulas for fuel increasing the distance of my ships. Let me mine protostars for energy or exotic materials to increase ship quality or structure quality.
Ships, Structures, and Combat:
Ships should ALWAYS matter. Constructors need to be able to do other things or rather we need new structures to make them a viable aspect of strategy without resorting to "armada of constructors to take a single weapon resource and swing the game." Production in space should be an integral part of the game. To start: Certain structures should be able to be constructed on planets, asteroids, and moons without a colony attached assuming the right technology is possessed. Let me construct foundries on my asteroids or moons (this will remove their production benefit to the planet, but then I can use them to separately power a starbase or the creation of a different structure which does not require a colony). Research outposts are another good one. But how do you balance this? Answer: Survey Ships. Before outposts can be setup (of any type: research, mining, production, trade, or military) a survey ship must scan the area. If the area has been "terraformed" in between survey, then outpost creation fails (a new survey is needed). Orbital Construction: Planetary defense grid (array of satellites which improve planetary defense); Planetary Observation Grid (increases Security rating), etc.
Exotic environments should require exotic colonization methods. Suppose my race is organic (earth normal) and gains the "basic radioactive habitation" technology. My colony might be an underground bunker shielded from cosmic rays. This will be the limiting factor for the colonies production/economy/etc. But an aquatic species might live in specially designed pools of radioactive absorbing semi-fluids with an aquatic core (water is a very good radiation sponge) allowing for a greater "initial" planetary quality (how much of the planet is usable) and less planetary output penalty. High end technology (not quite as high end for artificial life forms) should allow for artificial planet construction right along side the "terror stars." Exactly what prevents another race from copying a "Galactic Achievement?" Super Projects are fine (and as long as the tech has pre-requisites), then there is no need for "Galactic Achievement." I refuse to believe that only the Torians can construct an Aquatic Transport System. Certain things are not properly a Super Project either (Secret Police center should just increase Security). Trade Goods are not a Structure. They are a resource that is controlled and used. If you want to have "monopoly" over a resource, then you had better be the only one who controls said resource. Trading agreements can then be setup to arrange for "access to a resource" for a price. If you have no resources anyone wants other than "raw materials" then you had better have a service (like high production values or high quality values) or expect very monetary compensation for trade.
Traits should always matter. Ship Quality is a wash. It is precisely no different than Ship Weapons bonus. Ship quality should be a small bonus to defense, hitpoints, speed, sensors, miniaturization, weapons, and repair rate. This would mean that certain designs could only be created on certain worlds (due to quality bonuses). Experience Should Matter. Ship hitpoints going up due to experience is nonsense. Ship Security, Soldiering, Tactics Value (New Trait), and small bonuses to defense, speed, sensors, weapons, and repair rate are all valid.
Soldiers should always matter. I should be able to take over enemy ships (masters of orion). Thus Crew also matters. If part of my crew dies I should be able to replace them by getting (greenies from colony or outpost) or by sharing ship to ship (or possibly starbase). If I want to invade a planet or starbase without first taking out its defenses (ships and structures should matter), then I do so at my own risk. Planetary missiles may wipe me out, and they may not depending on my entry technology, troop ship defenses, and personal defense technology.
Planetary invasion options should be more varied and less uniform. The evil killing machines (Yor) should not be able to utilize information warfare right off the bat. The notion of lying about killing probably doesn't compute. Not all "invasion" options should require troops. Planetary blockade cuts off trade with a planet or stops other cultures from doing business with a trade resource (you might not want to destroy in the hopes that you can capture it with soldiers). There is no reason why a capital ship armed with missiles cannot engage in planetary bombardment (it may risk ground based defenses, but that is why it is shooting missiles at the surface). And if I want to use a combination of mass drivers and core detonation on a planet until it is just a pile of loosely formed rubble orbiting a star, then so be it. Sometimes victory is pyrrhic in nature.
Ships should be able to come to a draw. If my ship has 5 million attack and yours has 5 million attack, then so long as we both get a shot off, then both sides should be eliminated. Getting "first strike" due to Tactics should be valuable. Weapons should show differentiation. Missiles can bombard. Maybe mass driver weapons add to missile defense for a ship (thus allowing for missiles to do more damage and still have a standardized tech point cost for missile defenses). Maybe beam weapons penalize enemy sensor ratings thus decreasing chance to hit. This would also give reason to diversify the weapon complement of a ship. Extra Military Production should Not be wasted. I should be able to produce multiple small ships or one larger ship for the same MP cost. This would be simplified by expanding the starport number for a planet (thus increasing planetary defense and making ships valuable) and allowing ships to create "fleets" while in orbit (thus preserving screen space and making it easier to access rather than having to launch everything individually). And this opens up new strategies by allowing a race to specialize (somewhat like the Krynn) in smaller ships late in the game to fight larger vessels.
Modules should matter (having a larger crew complement for increased "security rating" thus preventing enemy troops from invading and resisting espionage). Sensors are notoriously ineffectual. Sensor rating should affect the Tactics rating for your ship/fleet, how much preparation time you have before a battle (your sensor/speed versus opponent sensor/speed) Support ships/modules should decrease the penalty due to being within enemy territory as well as increasing the range of the fleet (Yes Fleet). Command Modules (increasing the tactics rating of the fleet by having dedicated admiral) and Fleet Modules (allowing capital ships to transport smaller ships and expand the logistics points for that fleet; only highest fleet module benefit need apply for purposes of increased logicistics) should both exist. Modules (like technology) should always be gradual. Initial technology should not grant the best modules and then have lesser modules available later. Edit: Big Issue for me personally. You should not be able to see all ships/starbases within your explored area "magically." This is what sensors are for right?
Battle should be cinematic and turn-based. You tell your ships what you want them to do, and then they try to carry it out to the best of their abilities. Experienced ship captains and crews along with high tactics ratings will determine how well a given action is carried out. The tactics rating, prepartion time, and terrain will determine what options are available. Opponents will obviously try to avoid this (sensors, speed, tactics, will all factor in). Tactics rating grants a bonus to logistics, thus highly experienced captains/commanders are able to unify more ships together. Expand logistics values/increase capital ship logistics costs. A squadron of fighters should Not be difficult to manage. Intraspecies warfare should have managed to produce sufficient logistics that a squadron of fighters can be commanded before the age of hyperspace.
Races:
Major versus Minor traits. For campaign/permanent races only the minor traits will be customizable. Traits will include negative consequences (a race with hyper intelligence might have developed in a low gravity environment allowing for big brains but weak bodies and thus suffer a production penalty as a result). Major traits (some will have no cost at least for the first choice) will govern ecology, starting planet size, racial gravity/starting planetary gravity, economic model, religious model, political model/party, racial focus (research, military, commercial, social, civil with penalties though not as extensive as the planetary focusing) and racial bifurcation (ability to take on multiple government, religious, or economic models...); whereas minor traits will include small benefits used to "tweak" your race or tack on that extra 5% to your overall goal (so you can either take lots of minor traits or a couple major ones...). Creativity increases chance of "breakthrough" for all tech point related researching. Metacreativity (New Trait) increases the rate of advancement point accrual.
No Super Abilities. Super Warrior is more properly just a bonus to Tactics. Super Breeder is a race which has a Major Trait of Unusual Reproductive Rate (+50%) or something like that.
All "salient" abilities (logistics, tactics, miniaturization, ship quality, ship defenses, etc) should be able to be manipulated at the start if the player chooses. But the ability to use a "default" or "have the computer choose" should be an option.
Edit: Personal "Peeve" Units should not be earth standard. Metric Tons should be "Galactic Standard Tonne" or something like that...