Sorry to necro a thread, but another thread here on the Olsen twins reminded me of this, and a search brought me here.
A guy I know with a phd in psych is seriously into MBTI, and I think that's been a lot of his focus. He told me once that identical twins separated at birth (and often raised in drastically different environments) test exactly the same on MBTI. He said there's less variance in the MBTI results between separated identical twins than there is with the same person taking the test twice.
Of course, I can't seem to dig up anything on this. I'm going to ask him for his source next time I see him.