What part of the brain corresponds to our ability to laugh?

The limbic system is involved to a degree and in particular the hippocampus and amygdala. I think quite a few sub-cortical, primitive brain areas are involved.

 

This page has about as much as I know so it's probably eaiser to to read that:

http://en.wikipedia.org/wiki/Laughing

 

It's not too clear on this page but I think many of the areas they mention are actually involved in the physical production of laughter. Laughter is more like an involuntary action that can be modulated by top-down input form the cortex and limbic systems. (I think)

Ironically I found the link on the laughing page to this so funny

http://en.wikipedia.org/wiki/Tanganyikan_laughter_epidemic