It's not really a question of believing or not; there are good tests administered by qualified professionals and there's... everything else. Most internet tests fall in the latter category. Of course, you can still get something useful out of them, but don't take them to heart. Just see them as opportunities for introspection. Also, if the test has anything to do with personality disorders or other mental conditions, then you should definitely consult a professional instead of relying on them. Self-diagnosis can sometimes do more harm than good.
Incidentally, one of the most popular personality tests out there (at least on the internet and among non-specialists) is the Myers-Briggs Type Indicator, which is heavily flawed and therefore should be taken with skepticism.