Is the Myer Briggs Type indicator (MBTI) a reasonable scientific theory?
From what I remember, the MBTI has been compared in some studies to the Big Five (or OCEAN) model of personality. If you've not heard of it, the Big Five is the primary theory of personality that is accepted by researchers who do this sort of thing. Here are some papers comparing the two approaches:

Recent comparison and another.

The main point is that a number of the MBTI traits are correlated with the Big Five traits, though the MBTI can be criticised for various reasons (e.g., it's binary approach to personality). I think from what I remember is that the main criticism revolves around the fact that the MBTI has no place for neuroticism whereas the Big Five does.

That should be enough to get you started (e.g., reading their intro and seeing where this has been cited). There's also a somewhat useful infographic available here.