The following (in no particular order) are all games I've been addicted to at some point, typically defined as playing all through the night and not being able to stop.
Chess (Free Internet Chess Server). I love 1 minute games. Its really crazy extreme fun. This is one of the 2 that I will never quit.
I consider bughouse chess the most fun game ever. Imagine 4 pre-teen kids on a train, at night, two pairs sitting on opposing top bunks throwing chess pieces across to each other and shouting at the top of their lungs (that's how its played). I'm really lucky I never got thrown out of a train.
- Arimaa. This is a really cool strategy game. Its a pity so few people play it. I quit because their flash based interface is buggy and often crashes.
- Text twist. I'm quite good at this, my highest score was about 70000. Gave it up when I started exhausting all the words in the database :)
- Stick cricket. Its amazing you can make such an entertaining game with just two keys. My roomie is a god at this. Definitely top 5 in the world, probably top 3.
- Frozen bubble. Every self respecting linux user should have been addicted to it at some point :)
- Konquest - gets boring pretty soon because the computer AI is not very good
- Empire XP (windows) - same concept as konquest. AI is better than that of konquest, but you can still beat it after a few days.
- Samegame. I once scored 6600 after getting an amazingly skewed starting position.
- Breakout - I was addicted to breakout when I was about 6 (on an ancient console) at my cousins' place. I didn't quit naturally, so for more than a decade I had a craving for breakout. The first thing I did after install linux was play xboing for hours and hours. The level editor killed it for me. Later I was addicted to lbreakout2 for a while.
- Rubik's cube. This is the other one that I'll never quit. I'm quite good at this, my average time is less than a minute. Takes several months to learn, though. I use Victor Ortega's sequences with some modifications.
- Pacman - there was an old MD-DOS implementation called MS-PAC that was really good. I haven't found anything else that's decent. All the X-Window implementations suck big time. They're really astonishingly mind-bogglingly bad.
- Gtali. My highest score was 430. I got 3 yahtzee's in that game.
- Tetris. I was never very good though.
- Minesweeper. (I probably have the worst highscores ever. small - 5 seconds, medium - 40 seconds, large - 3 minutes).
- Maelstrom. Asteroids clone. This is one of the few games I was addicted for so long that I had to uninstall it.