... it depends.

What is my position?
Are opps reasonable or nincompoops?
How strong is my overpair? Was I the preflop aggressor?

Typically I will play out my overpair with the working assumption that it's the best hand until betting shows me otherwise. Note that this doesn't mean that I go crazy either...

I also tend to raise a fair number of hands prelfop (~ 10%) and tend to cbet them as well. This probably affects the way I play overpairs and how I'm perceived on the table.