Nope, I prefer offline games usually. I think some people may get addicted to certain ones because there is the illusion of progress and gain. Some games also allow you to gain loot and show off rare items to others, so add to that mix the feeling of pride and competition, then on top of that, add in the feeling of camaraderie and belonging to a group and you have yourself the formula for a possible addiction.
I played this online game called Shaiya once. It's the devil. After spending 2k$ I got banned.