There's no requirement to carry one, but in many states you must produce it if you are carrying it, and of course you need one to drive. If you're being cited for something, even something that doesn't typically come with jail time like say jaywalking, lack of ID usually translates into being arrested so they can "ascertain your identity".

Hiibel is the main precedent here.

http://en.wikipedia.org/wiki/Hiibel_v._Sixth_Judicial_Distri...