Oh heck, where do I start. I got hooked on the old Pong-style dedicated devices. Then we got one that had a tank game in addition to the Pong. Had an Atari 2600, VIC-20, C-64, Commodore Amiga, then finally got into Windows in 1995.
Most of the games since Pong are a blur. One game I loved on the Amiga was The Lurking Horror. There’s a board member here that goes by that name, but I don’t think I ever had the opportunity to ask about any connection with the game. It was an old-style text adventure, with the notable addition of spooky sound effects. The sound REALLY added to the atmosphere, and I’m sorry that no one did much more with that. Given that it used Lovecraft as a basis for the game, it was très spooky. I spent more time on my Amiga programming than gaming. I also got my start in playing with computer graphics in Deluxe Paint, something I dabble in to this day.
On my 2600, Missile Command was a fav. It was one of the few that, honestly, didn’t look like complete ass. There was a maze game called Wizard of Wor. Loved that game, and I’d play it for over an hour without seeing, “Game Over.” A couple times I turned over the point counter, and according to a magazine I had, I beat the world record by about 20%. No one to see it, no picture taken, oh well. 
When I first got my c-64, I stayed up all night playing Castle Wolfenstein & Zork. Teenage computer geek heaven! Other favs were Saucer Attack, which looked awesome (for a c64), Beach-Head and Raid on Bungling Bay.
Since moving to a Windows platform, it’s been a nonstop parade of first-person-shooters, with some first-person RPGs thrown in. Wolfenstein 3D, Duke Nukem 3D, Doom, Quake, Unreal Tournament, and a whole hell of a lot of Battlefield 2. The past couple years has been mainly Dungeons & Dragons Online, Fallout 3 & New Vegas, Borderlands 1 & 2, and hopefully soon, Skyrim.