Researcher Jake Mandell has created an online test which measures pitch perception as well as musical memory. The test plays two brief passages of very similar music back-to-back, and you press a button to indicate whether you think the tunes are the same or different. (Often the differences are subtle -- maddeningly subtle.) At the end of the test you can fill out an optional survey about race, sex, and age; data is collected anonymously and periodically analyzed.
The test is hard -- my professional musician friend got a 66%. You can take the test here, or read analysis of over 100,000 test results. Also interesting: Wikipedia on tone deafness. So: how'd you do?