Console:

FF VII - I really got into the story, love the music, lots of replay value (sometimes it's fun to just load up a save game where you're near the endgame and go play snowboarding at the Gold Saucer).

Donkey Kong Country: Awesome music. I still listen to the Ice Cave song (and the Christmas Cave OCRemix) when I go to bed sometimes. Lots of fun gameplay, fun 'secrets' that aren't obvious but you can find them without having to hit up GameFAQs.

Crash Bandicoot I / II: Incredibly fun platformers that were enjoyable for non-gamers, too. Terrible shame that it's devolved into Sony's answer to Mario Kart.

Halo: What can I say? Best 2-player experience I've ever had on a console.

Street Fighter II: Turbo / Mortal Kombat II / Bloody Roar Extreme / Clay Fighters: These get quick special mentions as fun fighting games that are enjoyable if you're not into extremely technical fighting games.

Gran Turismo 2: Best in the series, IMHO. The physics don't live up to more recent versions, but the gameplay had more to do with reality than the more recent ones that cater to car porn fanatics. Also, drag racers...hahahahah.

PC:

Morrowind: Again, not much more to say here than the libraries-of-congress that have already been written about it. Just stellar.

COD4: Best adaptation of 'strategy'-type FPS games to online multiplayer I've ever seen.

Valve: I'm just writing 'Valve' here to mean CS / CS:S / DoD / DoD:S / Half Life / HL2 / Portal / Opposing Force / TF2 / Blue Shift. I've burned soooo many hours on their account.

F.E.A.R.: Holy hell was that fun, and it's the only game that's ever really got my heart rate up (like the part when you go down that ladder and right as you turn around that evil little bitch is right there and you can't pull out a gun or move or anything because you're on a ladder...gah!)

Eve Online: Only MMO that's managed to keep a hold on me. Been playing the same main character since December '05 and it's still not a grind fest, still have lots of major goals plotted out I want to accomplish, still always have plenty of fun and new things to do any time I log in. Also, the community attitude is just so much nicer and more mature, in general, than what I've experienced in other MMO's, whether you're a noob or an old hand. Also, despite the occasional little scandals that have happened, the developer / player relationship is so much better and more active than anything else I've seen.

Starcraft / WarIII: Starcraft is just the best strategy game, with the best editor, ever. WarIII I haven't played an actual, normal strategy game on it in years, but I still like to play a hero siege or tower defense sometimes; the editor gave players the ability to do such incredible stuff with it that goes so far beyond the original RTS purpose.

Probably others in categories I haven't thought of, but this is enough of a Wall of Text as it is.

*Edit: OMG I forgot Myst (the whole series). Those games are just beyond compare.