OK I am an addict. Started in the 70's with an atari 2600. Run forward a bunch of teen years etc where I didn't game at all - then got a Game Boy and was addicted to tetris. Then got addicted to Super Mario Land and the entire Super Mario and Wario series. Follow the first Super Mario with Zelda. Best. Game. Ever! I LOVE the zelda series. I then dated a guy who was HUGE into gaming and introduced me to so many more.
I got an N64 with many games. One of my all time favourites is Space Station Silicon Valley - not many seem to have heard of that but it is brilliant and has much hidden comedy in there.
Then came Everquest, very very addictive and I put this addiction down to the cause of the break up of our relationship. So my "game boy" departed and I carried on. I have a Game Boy, Game Boy Advance, Game Boy Color, Game Boy DS and the other one that folds in half. I've not played game boy for quite some time.
After Everquest was Dark Ages of Camelot. Then, I was invited in to the World Of Warcraft closed beta. I finally quit the game in March and took up knitting.
I recently bought a PsP too which I LOVE - I have yet to downgrade the firmware on it to play homebrew games but I'm going to do that soon.
Other favourites: Rayman, Kuru Kuru Kirikin (or whatever it is called - puzzle game for GBA), Silver (and old PC game), Thief. I love RPG's, platformers and adventure games, I also love puzzles that test your reactions. I am not so keen on Sims / Civilisations type games. I have Black & White 2 which is ok but I just get fairly bored with it fairly fast. I prefer things that constantly change, so platformers and RPG's for sure.
Edit: OH! I also have a game cube. Can't wait for the new Zelda later this year - it looks awesome!