Persoanlity testing is looking for "underlying disorders of thought" and sometimes belief patterns. I would not consider the Meyers-Briggs or the Strong clinical instruments. They are normed on "normal" populations. However, this does not mean they do not yield interesting information--just not diagnostic information.
The MMPI is very clinical and if the person is truthful, it picks up personality disorders, as well as traits that do not rise to diagnosis very well.
I detect some confusion in this thread. "Personality tests" are directed at constructs that are not nearly as objectively demonstrable as something such as ADD. The Rorschach (ink-blot test) is only as good as the person interpreting it. That could be said of an objective rating scale such as the BASC or Conners' also (if you make scoring errors, the results will not be valid.) However, the Rorschach's interpretation is very sujective. The interrater reliability between independent scorers in not good. That is why you want someone who is well trained and uses the Rorschach frequently for it to be valid. Personally, I would NEVER let a school psychologist administer a Rorschach to my ex-difficult child, and they certainly wanted to.
Just my .02
Martie