This thread makes me happy like a maniac. I'm going to have to mostly just second things here since everybody's posted great stuff.
Secret of Mana was huge for me. The whole Seiken Densetsu series has been, in fact. One of the first games I ever truly loved and I still play the games from the series regularly. In fact, I'm going through Legend of Mana again right now on my PSP thanks to magically delicious evolutions in the community of late. Oddly enough, I'm also going through the Ecco games again. I have to agree with Krissy, those are still some of the most amazing games I've ever played. And HARD AS HELL. Man. Without an emulator I still get slaughtered regularly playing those. It's emotionally draining. But I've still never played anything else even remotely like them, and they're so much fun and so beautiful. Doom was huge for me too, of course, and Quake.
Here's one that I lived on:


Descent, baby! Descent 2 I didn't get into quite as much, though I did play a pretty good bit of that online via Kali.


Descent 3 had some great stuff in it too, especially MP. SP was a bit more of a mixed bag, but I still loved it.

And can't forget the Panzer Dragoon series!



I never got to play Saga. =( Been looking for a copy for years and years now, but I'll be damned if I can afford that kind of cash.
SYSTEM SHOCK! I can't believe nobody's mentioned this one!
And System Shock 2, of course.


I can't wait for BioShock. Going out of my head waiting for that one.