Reading through this thread was fun! It kept me in suspense, and I almost cheered when Deus Ex, NiGHTS, and OMF 2097 were finally mentioned!

Unfortunately, it's driven me to a long response, so just read the bolded stuff if you want.

So yeah, the original
Deus Ex is without a doubt my favorite video game of all time. I thoroughly enjoyed the second one, but the first is just way above anything else I've ever played. I love every part of it; the story, the dialog, the characters, the music, the graphics, ... even the rediculously forgetfull AI that could only turn in one direction! I've memorized the intro dialog and have lost count of the times I've played through it. My last runthrough about half a year ago, I was still finding new areas and new branches of dialog and was still getting scared silly by
those karkians! And the bunker level (post-nuke) in particular gave me several "whoa" moments. Good times. Can't wait for the third one.
The list of other FPSes I've enjoyed would be huge, but the most memorable are the original
Unreal and
Rise of the Triad. My favorite moment in Unreal was when you come out of the ship in the beginning and are
greeted by a huge, lush (for back then), outdoor environment. After being cooped up in the likes of Doom and Quake for so long, at this, my jaw decided to go walk around the house for a while. ROTT was cool and inventive in so many ways and
weird and funny in many more. (Yes, the game really shows that picture and message if that error is encountered.) There's a great article on its weirdness
here if you have a good chunk of time to waste.
Then, for anyone who doesn't know about the original
NiGHTS, you flew around in 3D environments (constrained by various paths through it) collecting orbs and fighting enemies and bosses. However, you could also run out of flying time or choose not to fly at all and instead go walking around the world with complete freedom. Even though that wasn't the point of the game, there were things to interact with in the world that were only accessible while walking. You could also breed some of the world's critters and cross-breed them with the enemies, but I never got into that. Mostly, it was just inexplicably fun to play.
Of the racing games mentioned, I remember being impressed by the demo of
Slipstream 5000, but I never got the whole game. I do have
Ballistics and
Hydro Thunder, however, and they were loads of fun. Ballistics wasn't a particularly long or deep game, even as racers go, but its unlimited speed was sooooo much fun. I always look for Hydro Thunder when I go to an arcade, but the N64 version was great fun, too. It had some really imaginative environments, and racing on the water just felt completely different from other games in the genre.
I still play
One Must Fall 2097 in Dos Box when I'm in the mood for some good mindless action. And one of its cheat codes makes nuts and bolts and scraps of metal fly all over the place when you hit eachother.

Which reminds me: ROTT has a similar code that would create "Ludicrous Gibs!" every time you hit someone with a missile.
Full Throttle was another great game, but I wish its puzzles were more forgettable so I could solve them again. Regardless, it's worth playing again and again just to hear the main character talk.

Then there's
Morrowind. Ah, the hours I've
wasted spent completely immersed in that world. Then I found a mod that hugely improved the atmospheric sounds and became even more immersed. I've not had much chance to play Oblivion, but what I have played of it seems even better in some ways.
Super Metroid has been mentioned a billion times so far, so I'll just name it as one of my favorites.
I'll finish off with some RPGs. I've never played any Final Fantasy games, so my Square experience points come mainly from
Chrono Cross and
Mario RPG. Mario RPG was just plain fun, and its hidden Final Fantasy boss stole the music from FF4, so I might have to get that DS cart one of these days.
Chrono Trigger was fun, too, and I did play it before Cross, but I think Cross's music won me over. It just made everything. Not that it wasn't a fun game besides that, but I love me some good video game music.

*cough*
Aquaria*cough*
Radical Dreamers (translated from the Japan-only SNES satellite game) was also awesome (especially when played at night), and its music and relative lack of visuals let my imagination go to work, almost as if I was reading a book...with music to increase the atmosphere.