This was advertised on a BBC show a few weeks ago, although I believe the test dates to last year. It's not be up much in the last few weeks I think because of a problem with a section of the BBC servers (rather than the test itself) ...now it's working again, and should remain so, but if not, don't keep trying too frequently.
This is a Big Five test. On top of your score in each trait, you also get some other feedback. Unfortunately you need to register.