Galaga, I only quit when I run out of quarters or juice.
Tetris, especially Tetris Worlds on the PS2 since it seems it just keeps adding extra time to the time limit for eternity. I still don't understand why exactly.
Yu-Gi-Oh games, especially the GBA ones.
Oblivion, I'm hesitant re-install it.
Princess Maker 2 until I finally got the Princess ending. Completely dropped it after that, even though I could go for other cool endings.
Back when I played Attorney Online with a certain group in its prime time, I would stay up every weekend playing it, and for many days if I was on break. Games could go anywhere from 2 to 6 or 7 hours, a few special ones even a little longer. Thank god for laptops I can take with me to the kitchen and bathroom.
Was also super into Luna Online and Eden Eternal, but LO shut down a while ago and EE is as good as dead, unfortunately. I still play on a private server on Runescape, but I usually play while doing something else, so I don't know if it counts.