It's very difficult for me to arrange 10 games into a specific order. I can give you the ten, but don't ask me to tell you which I believe is better then others - they're all great in their own unique ways.
Half-Life - This one still holds a place in my heart - if I had to pick a number one, it'd be this one. It's just everything a perfect FPS should be, and if you look around and replace the models, it can still holds its weight against modern games.
Super Mario 64 - I recently replayed this - it's still untouched, even by its sequel(s). An absolute joy to play and absolutely everything a platformer should be. We need more games like this. Well, good ones, that is. Incidentally, what's the DS version like?
The Legend of Zelda: Ocarina of Time - I have many a fond memory of this. Really should play the master quest sometime... It took everything that was great about the 2D games, put it in a 3D world and then made it even better. Absolutely amazing.
Sonic 3 & Knuckles - The best game of the series. I still have the zones memorised through and through. The series went downhill from here, but we still have the ultimate rush of making that run from one end of the level the other without stopping ONCE. That's why the DS one works - Sonic is about SPEED.
Final Fantasy VII - Yes, the sequels may have had better stories, graphics, etc. But they didn't have big kickass swords now, did they? Plus, I can admit to crying when playing it, something I can't say about many games.
Grand Theft Auto: Vice City - It was the ultimate collection of everything that was fun in GTA3 with all the glory of the 80s and none of the realism of the sequel. This is better then San Andreas, whatever you might say.
Goldeneye - I own at this in multiplayer, and I think that says it all, really. I have a thing against console FPS', but this was everything the genre needed at exactly the right time. The Doom II port was nice, but the sooner this is remade in the Source engine, the better.
Conker's Bad Fur Day - I think the only times I've laughed harder at a game were with Sam & Max and Monkey Island, and even they never dared to go as low as this game. It may have been somewhat frustrating in places, but what other game has you pollenating a sunflower? Also - is the remake as good as/better then/worse then the original N64 game? Just curious.
Chrono Trigger - I have a problem with RPGs. Even with the best ones, I can play so far and then just... get bored and drift away. Not so with Chrono Trigger. No random battles (you know what I mean), a compelling story, a lead character THAT NEVER TALKS and, best of all, NEW GAME +!!! More games need that option, they really do.
Monkey Island - They're all so good it's hard to pick one, but if I had to, I'd go for the second. These are some of the funniest adventure games you'll ever play, and if you haven't tried them you deserve to be smacked about the head with a rubber chicken with a pulley in the middle. Pure genius.
Honourable mentions go to: Sam & Max Hit the Road and most other LucasArts adventure games, Planescape: Torment, Deus Ex, every other Final Fantasy game, Unreal I, II and Tournament, every other Zelda game, the Banjo-Tooie series, the Jak (and Daxter, according to the original game) series, the Breath of Fire series and the Star Wars Dark Forces series. The sooner they finish that remake of the original for jedi Academy the sooner the gaming world can have a collective orgasm.