Games I was/am addicted to:
Peggle Dual Shot - pretty much played it until 100% completion night and day
Big Bang Mini - I love this game oh so much I want to kiss it with tongues.
Henry Hatsworth - Up until the very last boss I seriously was putting hours a day into this game.
Antelier Annie Alchemist - I love the crafting/alchemy system and the characters were fun. The game was a bit on the short side, though. Still, I actually played through it twice for different endings which is something I've never done before.
All Cooking Mama Games - I tend to play them until I perfect all recipes then move on. I didn't care for Gardening Mama, though. Sushi Academy was the same way, as that's pretty much just Cooking Mama with a Japanese coat of paint.
Any Time Management Game - I don't know why but I love a good time management game. I actually played Burger Island and Fast Food Panic until I beat them. Diner Dash and Hysteria Hospital are always at hand for me to play until I beat those, too.
And now the weirdest game I was addicted to ever: Puzzle Kingdoms. I realize it was just a low production value piece of semi-shovelware made from the remnants of Puzzle Quest, but I loved the puzzle system and had fun playing it until I beat the game. I enjoyed it way more than Galactrix or Gyromancer on the DS. Hopefully Puzzle Chronicles from Konami leans more in this direction than Gyro.