First game I ever played was on my cousin's SNES, first console I ever owned was the Sega Megadrive. Sonic 2 and Vectorman rocked, still go back to them every few months.

After which I got an N64 with GoldenEye (in my opinion one of the finest FPS games on any system - console or PC). Legend of Zelda: Ocarina of Time is less a game and more an adventure (got it again off Ebay before Christmas and am currently playing it, last time I played it I had borrowed it off the same cousin that introduced me to gaming), I also have the sequal, Majora's Mask which is almost as good. Not to mention Perfect Dark (only thing keeping it from topping GoldenEye in my books is that you are not James Bond), and Lylat Wars (a great flying shooter, sequel to StarWing on the SNES).

I then got a Sony Playstation and have Final Fantasy VII, VIII and IX on it as well as MetalGear Solid (the best in the series in my opinion).

Finally I got the Nintendo GameCube. Super Smash Brothers Melee is an excellent beat-em-up. Pikmin is a great RTS and is extremely different from any other RTS on the market, one of the best around. Star Wars: Rogue Squadron 2 - Rogue Leader is a brilliant Star Wars game, one of the best if not the best Star wars games out there. I love defending Hoth, seeing the hundreds of troops fighting it out below as I fly past them and keeping the hundreds of TIE fighters off the capital ships during the battle of Endor.