Bit late to the party, took me a while to think of this and type it out, probably missed a few games anyway.
My favorite genre is 3D platformers, which as Moon Monkey said, is a dying breed of games sadly. Banjo-Tooie is my favorite game, Rayman 2 comes in at an extremely close second. EarthBound/Mother 2 is my favorite RPG, though I'm not a huge fan of them since turn based combat is a load of bull, I do make a few exceptions if the rest of the game is excellent. Super Mario World is my favorite Mario, none of the other 2D Mario games can top it, though many say 3 is the best, World took everything in 3 and multiplied it by awesome. Plus, Yoshi. Sunshine would have to be my favorite 3D Mario, ironically, since it's the most hated, but it was the last free roaming type of Mario game, and it's generally better than 64 in every way, I never had a problem with F.L.U.D.D. either. 3D World may not be free roaming, but it's looking like it'll be one of the best Mario games in a while, I did love 3D Land and for once Peach isn't kidnapped but actually playable in a main game since Super Mario Bros.2/USA.
Majora's Mask has to be my favorite Zelda game, and probably my third favorite game in general, sure it didn't have many dungeons, but the side quests really shined, and the feels throughout the game man, the feels. A Link to the Past would be my favorite of the 2D bunch, gameplay wise and mechanically speaking, it's probably the best of them. As for 2D platformers, Sonic, DKC, and Rayman are all in my top list. Portal is my favorite first person game, though I generally don't like those games, and I really, really dislike shooters. Honorable mentions to Kingdom Hearts 1 and 2, Vexx, Jak and Ratchet, Glover (god this game), old Spyro, a ton of old arcade games (Dig-Dug yay), and Journey, oh man Journey.