The Diehard Test Suite is something close to a Golden Standard for testing random number generators. It includes a number of tests where a good random number generator should produce result distributed according to some know distribution against which the outcome using the tested generator can then be compared.
EDIT
I have to update this since I was not exactly right: Diehard might still be used a lot, but it is no longer maintained and not state-of-the-art anymore. NIST has come up with a set of improved tests since.