I could make a REALLY long list...
Super Mario 64, for one. It was just a really good game, but I eventually got all the stars and got done with it.
Age of Empires. My first RTS game, and it was bloody good.
Pokemon. I came. I saw. I caught them all.
In four separate games, I might add.
But, That's all in the past. My most recent would be...Guild Wars, I guess. Great, great game. It's not so much an addiction, "I MUST PLAY" thing, as is is an annoying twinge to go and play right now. All the time.