If you're using DOSBox 0.74 on Mac OS X, please hop to the DOSBox site and download DOSBox again.

See VOGONS/11th Hour crashes on startup dosbox 0.74 for details.
In this thread, Dominus wrote:

If you have downloaded dosbox 0.74 some time ago, please download it again as The OSX version was updated just over a week ago. On OS X 10.7 and above it crashed on going fullscreen because of an incompatibility of SDL with those OS X versions. Now that dosbox is compiled with a newer version of SDL it runs ok. If you use output=opengl it should be fine, too.

Tech stuff, taken from the Changelog file:

0.74-1
Special OS X Version
- built against SDL 1.2.15 which fixes going fullscreen on OS X 10.7 and newer
- includes the following DOSBox revisions:
- 3689: Fix startup detection of numlock and capslock.
- 3694: Update CALLBACK_Idle to use the callback offset. Fixes memory corruption.
- 3776: Fix bug 3477126. Don't put junk chars in the title bar. Mac OS X will crash on it
- 3777: Add cmd-q => exit for Mac OS X

It is codesigned for Mt. Lion as well.