We watch a lot of movies, because DD has a long attention span and movies are usually of a higher quality than random kids TV shows, with more complicated story lines and more sophisticated character development etc (depending on the movie of course, I only go for what I think of as 'good' movies!)
We use common sense media, too, though I go for a year or so older than DD. It also has good lists of movie suggestions.
Aquinas, we love The Incredibles but I always feel a bit squinchy at the guy-jumping-off-a-building scene - I don't really want to explain that frown
We don't really limit screen time because DD tends to self-regulate anyway. Sure she may spend a whole week glued to the TV, or a game, but next week she'll be reading her history books, and the week after building a weather station outside, so I'm happy to roll with that