Funny, I didn't know any of them but Doctor Who?, and even then mostly as a cultural phenomenon - which is why my vote was cast on that. And then Dr. House, mentioned by Trizor, but to be fair I've never ever really watched a single episode after all.

If it were for me, the best doctor is The Doctor. Eventually, rumors are that some Perl 7 code is hidden deep inside his holographic subroutines. Probably this is much more relevant to his outstanding personality than is generally acknowledged.