Pyweek (make a game in Python in a week) : http://www.pyweek.org
TIGSource compos (make a game in about a month, game-makers are allowed so you might think this is lame): http://forums.tigsource.com/index.php?board=9.0
GameDev.net contests: http://www.gamedev.net/community/contest/
Retro remakes (currently recovering from a cracking attack): http://www.remakes.org/
"Gamma" series of compos : http://www.kokoromi.org/gamma/
Unfortunately they are all inactive at the moment.
Also there are "Game Jams" which occur in-person and usually aren't a proper competition, just an attempt at getting together and making cool games.
Examples: TIGJam, Indie Game Jam (deceased), OLPC Game Jam
Pyweek (make a game in Python in a week) : http://www.pyweek.org
TIGSource compos (make a game in about a month, game-makers are allowed so you might think this is lame): http://forums.tigsource.com/index.php?board=9.0
GameDev.net contests: http://www.gamedev.net/community/contest/
Retro remakes (currently recovering from a cracking attack): http://www.remakes.org/
"Gamma" series of compos : http://www.kokoromi.org/gamma/
Unfortunately they are all inactive at the moment.
Also there are "Game Jams" which occur in-person and usually aren't a proper competition, just an attempt at getting together and making cool games.
Examples: TIGJam, Indie Game Jam (deceased), OLPC Game Jam