Character... that's the thing I enjoy most in a movie, TV show or book. Show me a well rounded character and I'm happy.
It doesn't have to be a sickly sweet, white hat hero (in fact, that's probably the WORST kind of hero in my book :)), but if a character is believeable, flawed, makes mistakes, grows and develops as the story progresses, it'll do nicely, thank you!
A lot of thought SHOULD go into character "design" for a movie, and (it goes without saying) a lot more thought into any ongoing series! The audience has to be able to empathise in some way with the portrayal; make it too artsy, too incomprehensible, too vulgar, etc, and you risk losing the interraction with the viewer.
Never give away too much about the character in an ongoing series, at least at first; let the viewer see the broad strokes of the part in the first viewing, so they get a rough idea of that role in the production. Then, and ONLY then, start peeling away the layers until (eventually), the audience knows that character almost (if not better, at least as well) as themselves. Stand their preconceptions on their heads (if the story demands it and if the Character would believeably do those things); make the viewer CARE about what happens to that person (animal, etc; don't be constrained by what you "HAVE" to do). It doesn't matter what the story is, without well drawn personalities, the best tale will fall flat.