This is definitely a recurring discussion topic, but I think it's definitely one the developers left ambiguous.
There are a couple of points in favor of the "Captain is a normal person" theory, which involves two events: first, the Slug captain who tries to get the player captain themselves to drink something, and second, a Mantis sector boarding event which specifically says "you, the player" ready their pistol:
http://ftl.wikia.com/wiki/Slug_Captain_ ... to_a_Drinkhttp://ftl.wikia.com/wiki/Mantis_BoardersThese could be chalked up to questionably-accurate flavor text, but the text is in the game and it must be considered as evidence (however weak) against the "player is the ship's AI" theory.
Really, though, I think you can pretty much take whatever theory is your favorite.