Do internet games count? Then I would say League of Angels. Since I'm on so much, I can't help, but play it. It also helps that they have rewards for being on daily so I would just go on to get the rewards and end up playing the game anyway. If not, I would have to say Harvest Moon More Friends of Mineral Town for Game Boy Advance. I'm not sure why, but this game is so addicting. It's not affected by time whatsoever. I just play it because it's fun I guess.