Battlefield 1942 and subsequently Battlefield 2. Seriously, I was a full-on addict. I didn't have a computer good enough to play either so I'd go to an Internet cafe. It was at first just with friends, then it was alone, then I was literally nicking money so I could top up my iCafe account - I have no idea how much money I would have spent on those games but it was a lot. I'd come home late because I'd be at the iCafe playing the game. My folks thought I was on drugs.
I'm not joking either. When I started University I'd skip lectures to go to the damn Internet Cafe. It all stopped when I saved up to buy my own computer. That was in 2006, still in my first year of University. After that I played in a far more casual way, probably because I knew it would alway be there waiting for me if I wanted to play it instead of knowing that Hell, it's only at this place and not at home so whenever I get the chance to play it I need to TAKE that chance. Cured me of my crippling addiction anyway and I'm damn thankful for it. I've never been addicted to anything like that before or since and it was kind of scary just how controlling it was.