1st Gen: Before my time
2nd Gen: Intellivision. The very best implementation of Burgertime ever. Also the best implementation of Bump and Jump. And I preferred Beauty and The Beast over Donkey Kong.
3rd Gen (8-bit): Nintendo Entertainment System. Tetris, Castlevania 2, RC Pro Am, and Super Mario 1, 2, & 3.
4th Gen (16-bit): Didn’t own or really play anything in this generation. Got to play Super NES and Sega Genesis at friends houses, but didn’t love either as much as Tetris on my NES.
5th Gen (64-bit): Nintendo 64. Defined by Goldeneye, but I didn’t own a N64 until just a couple years ago.
6th Gen: Xbox. In fact I believe I purchased a copy of Halo before I bought the console.
7th Gen: Xbox 360. The first console I pre-ordered. Also the first console I purchased a replacement when it broke.
8th Gen: TBD