This question covers why Starfleet isn't terribly keen on intelligent starships (M-5 being a prominent example), and why there hasn't been much in the way of advances in the field, in-canon.
However, I'm curious about the expanded universe. Do any expanded universe works feature the development of intelligent starships, or starships that develop their own intelligence? In particular, do any of them feature a Starfleet starship with advanced AI capable of independent action and thought? Especially, ships developed past the end of TV and Movie canon, or that develop their intelligence past that point in time.