No way I'm going to write out that many, but I'll just make a small list of games that had an impact on me in some way:
Pokemon Red/Blue - first games I were ever really hooked on, parents finally gave in and bought me a Game Boy because I wouldn't shut up about it
Gran Turismo 3 - first realistic racing game I played
Katamari Damacy - random, but strangely fun as hell
Silent Hill 2 and 3 - my first survival horror games
Halo "trilogy" (1-3) - before they started milking the series for everything it's worth
Resident Evil 4 - hated the controls in the previous games which kept me from enjoying them fully, so this was the first one I really liked
Fatal Frame 2 - fucking scary-ass game, more than any SH or RE
Portal - showed you can still make a great game even without a ton of action scenes and whatnot
Team Fortress 2 - only online game I ever played, too bad they made it too complicated by adding too much new shit
Bioshock - incorporated great graphics, storyline and gameplay. One of the most "complete" to me in that regard.