In 1982-1984, I played a lot of arcade games, my cousin's 2600, and our Radio Shack TRS-80. The TRS-80 was a monochrome computer and most of its games were direct knockoffs of popular arcade games like Pac-Man, Galaga, Space Invaders, or Scramble. The first video game I can remember playing was Donkey Kong.
1984-86 we had a TI-99/4A computer. It had unique games like Tombstone City, arcade knockoffs like Car Wars (Dodge 'Em), Munch-Man, and TI Invaders (you guess what games these were aping).
1986, my mother got an Atari 130XE. Best gaming machine of the 1980s other than the NES. I had hundreds of games for it that my uncle acquired from me through "warez" organizations, LOL. Among other things, it had the best home version of Donkey Kong ever made (far better than the half-assed NES version) as well as some RPGs.
1987, my best friend got a NES with Mario, Zelda, and Metroid. I was hooked on Zelda for months and also played Zelda II when he got that. But I never had my own NES.
1989, I got the first console of my own, a launch Game Boy, for Christmas. Loved that thing. Came with Tetris and Super Mario Land.
1991, got a PC. Horrible sound and its action games were nowhere as good as console or arcade games, but I loved games like SimCity and PC-Hack (precursor to Nethack). Also into Ultima. In the arcades I played Konami's licensed beat-em-ups and the first edition of Street Fighter II.
1994: SNES bundle with Zelda for Christmas, also got Mortal Kombat II, Zombies Ate My Neighbors, and Battle Clash for my birthday. A year later, I got Donkey Kong Country, Final Fantasy III (VI) and Super Metroid. Still have the SNES and its games.
1996. Nintendo 64 with Super Mario 64 for Christmas. Was playing Virtua Fighter 2 in the arcades.
1998: The PlayStation, the first console I ever bought for my own, with Final Fantasy VII. Loved all the RPGs and still have most of them. Got Ocarina of Time on N64 and a Game Boy Color for Christmas.
2001: PS2 with GT3. Got Final Fantasy X the day after Christmas, Virtua Fighter 4 shortly thereafter. Bought a lot of games for it, too. Also got a Game Boy Advance.
2003, birthday: Gamecube with BloodRayne, Skies of Arcadia, and Zelda: Wind Waker.
2005: DS on my birthday.
2007: Wii and Xbox 360. Loved the Wii and enjoyed the 360 until it crapped out from the E74 error. It died right after the one-year warranty was up but before Microsoft started covering E74 under its three-year warranty for the RROD. I bought a used 360 rather than pay Microsoft to repair it, but after that, I was kind of done with the Xbox line.
2009: PS3. Got it for Valkyria Chronicles, along with a lot of other games.
2013: Wii U, 3DS and PS4.
2014: PS Vita TV.