I guess this would be the vote for Pokémon in general, seeing as they're all essentially the same game. However, up to now Blue is the only Pokémon game I'd played, and for several weeks after it came out I barely played anything else. I used to think that everyone only had one game of Pokémon in them, and Blue was mine. The subsequent versions have come and gone without registering any interest, but I think it was more me blocking out the fact that if I started into another it would consume me again. I'm currently finding that this is true with Diamond - my first new Pokémon experience since 2000.
What people tend to forget is that it's a fairly traditional JRPG, only with the Pokémon levelling up instead of the player character. The story is spare, but it's not important. What is important is the overwhelming compulsion to fill that Pokédex and capture every last creature in the game. The combat is actually quite a deep spin on rock, paper, scissors, and some of the set-piece battles take some serious strategy and forward-planning.
This became my RPG fix away from home. I walked to and from work with my eyes fixed on the screen, played it surreptitiously under my desk, handed it over to a friend when it came to the end of my lunch break and I was in the middle of a battle... yes, it's fair to say I was pretty addicted to Blue. And yes, I caught them all.