Dune. The original, not Dune II (also know as Dune: Battle for Arrakis i think) nor Frank Herbert's Dune (2000-something?)(game, not the miniseries of course. Yes, i know, it is obvious and i am rambling). The CD version has some damn nice graphics, the musics in that game are among the best i've ever heard, the desing, the look is PERFECT. And it is adventure/RTS... Actually, on personal scale, i'd say it does fulfill all four points, despite having played it after some more advanced games (considering i'm born 21 years ago (birthday today, April 13th!) it would've been hard to have played this before some others). Groundbreaking for me. This is the game that shaped my vision of Dune's visuals. It is a prototypical RTS... Ur-example of RTS games maybe? With Dune II being the genre codifier (or just another ur-example). Awe-inspiring: the looks, the music, the best adaptation of Frank Herbert's masterpiece in my opinion. Memorable of course... I wouldn't be writing this if it wasn't memorable. Originality is a bit hard but... as a game, yes i think it was pretty original. A mix of RTS and Adventure, adapted from a book which is quite hard to get right...
Funny. Dune II is not in my list of awesome etc. games. I played Dune 2000 first and Dune 2 just feel like a pale shadow of it's remake. I have no nostalgic feelings of course... but even if i had played it before D2k, i doubt i'd like it better. I'm not a nostalgic type, not really... i dislike that feeling. Dune 2000 is not original nor groundbreaking. Nor it was very awe-inspiring nor memorable since it didn't get very good reviews. But for me (and some others based on Youtube comments) it is awe-inspiring and memorable. I got it as a birthday present (did i turn 10 then? I cannot recall that) and being a Dune fan... No words for it, just love. (Now that i think of it there might be some nostalgia here but i do reinstall it every now and then and play it and it still feels fun and replayable, i don't feel nostalgic when doing that)
Civilization II. Do i need to say more? Again a sequel i've played before the original... though in this case i've never played CivI though i think i've seen my friend to play it. *Shrugs* An important game for me though the sequels are better games and i really don't like to play CivII anymore.
Alpha Centauri. Like CivII, only way better. Actually, i like SMAC (+SMAX) better than CivIII or CivIV (don't have CivV yet, waiting for a price drop, maybe an expansion and better computer). Really alien world, interesting civs (being based on ideologies rather than a culture/nation), damn good writing/quotes/stuff, terraforming taken up to eleven... Not quite ground breaking and originality is a bit questionable as in its hearth it is just another civilization game but still... The best of Civilization series.
Blizzard games (Diablos, Starcrafts, Warcrafts). They get only this entry.. Not all of them fill each point except maybe "memorable". Dunno, there's just something special in Blizzard's games.
Command&Conquer series. Especially under Westwood... CnC Generals is C&C in name only but still quite good. Classics, fun games even though the latter ones suffer from stagnation (CnC 3, almost like remake of the original), wrong style and direction (RA3) and a stupid try to re-invent the series gameplay-wise (and damn bad cutscenes) (CnC 4).
Halo Combat Evolved. The first Halo's title, "Combat Evolved" is true... sort of. AFAIK, none of its features (quick use grenades, melee and regenerating health) were original but their polish and combination with good shooting and good weapons did popularize them (and console shooters) and evolved the genre. Of course there's a drawback... FPS genre has stayed the same for a decade. Time to move on really. Back to the game itself. Open levels, large scale, good AI, really good and mysterious feeling enemies, great visuals... In retrospect, the game does suffer from lack of good and original story and the latter levels are not very good nor fun. The sequels are good too though all of them have take two steps forward and one back. Except maybe in Halo: Reach's case where it took two steps forward and one and half back, with the remaining half step being the visual upgrades and techical upgrades...
Mass Effect, 1 and 2. The first one isn't a very good game in retrospect nor did it have very original plot (quite similar to Star Wars KOTOR's (which BTW gets bolded for being an important game for me) but its visual and sound desing, the world, the characters... and even story even if its plot wasn't new one. BioWare's blessing and curse... they do play with tropes well but they really don't make new ones nor do they twist them in completly unexpected ways. Oh, "Ur-example" links to TV-Tropes which explains "trope" if you don't know what they're (or have only a vague knowledge) but be careful there... Search for TVTropes Ruin Your Life and you'll understand.
Battlefield 1942. Seeing an aircraft carrier driven to a beach, people sniping and firing (and hitting with) rockets at planes, jeeps carrying a squadfull of people and driving to mines, single handedly clearing and capturing a heavily defended capture point, awesome flying, infantry rushes, tank war, a battleship duel in which the side with more engineers repairing their ship wins, Desert Combat mod... Classic.
And finally: The Elder Scrolls III: Morrowind. Got this one from sale and... well, it was probably the best deal i've gotten. Where to begin? Open world sandbox RPG, very interesting alien-feeling world, very interesting lore, great visual desing, awesome music... and of course, the mods. Better than its sequel, Oblivion though the fifth game of the Elder Scrolls series, Skyrim might beat it. Might. Morrowind is... well, Morrowind. Sort of polarizing game really, you either love it or you hate it, there doesn't seem to be middle ground really. The same seems to apply Oblivion as well.
Of course ther are others but i can't stay up the whole night listing them and writing something about them.. And these are probably the most important ones for me.