My parents were really careful about what they allowed us to watch, and the often previewed a movie so they could figure out which parts might need to be skipped over. Though this may sound overprotective to some, I think it was wise of them to understand that children's minds absorb a lot more than one might think. Conversly, though, I'm also intrigued by the number of things went completely over my head (subtle innuendoes, for example) as a kid.
I have been dumbfounded recently by the number of young children at PG-13 movies. At this point, I might be less concerned about the influence of movies on adolescents than I am about the influence of movies on children much younger.
As with anything, I think a good deal of discretion should come into play when choosing entertainment. There are movies that have great content amidst less-than-good. There are movie studios, such as Walden, that try to make movies the whole family can watch, and there are movie studios that make money with the fairly recent brand of raunchy comedy. There are studios that produce movies with objectionable content that still tell stories that need to be told. There are the movies produced by church groups that mean well and sometimes fall short aesthetically. There are many choices, and one must be wise about making these choices.
I can't speak to the topic as a parent, since I don't have children, but I have seen parents who talk with their kids and adolescents to help them understand the difference seemingly insignificant choices (such as going to a movie) make. If the parent prohibits a certain movie, he or she gives a good reason for it. And choosing a movie becomes a moment in which the parent and child can dialogue about how movies affect us. It seems like a good strategy.