Users of the StarCraft 2 Beta have been reporting issues with the game locking up and various crashes. The big surge of the incident has been reported after the recent patch 11 had come out. When an update patch with the rememdy will be out is still unknown. Most of the crashes are not game breaking however, like the game-exit crash.

If you are playing the Beta and you experience a crash, a down and dirty fix for the time being would be to simply log out of StarCraft 2 before quitting the game.

Blizzard quotes:

We are aware of an issue that causes crashes upon exiting both the StarCraft II beta client and the Map Editor. This will be addressed in an upcoming patch.

Read further details at BattleNet Forums (thread here).

This being said, the game seems to be running fairly smoothly for a BETA. Considering other releases of such games have not gone off with such ease.