What is the furthest limit on a movie for which a child can watch?

My son and daughter are reaching the beginning stages of teenage years, and I think it is only fair to let them have more of a variety in what the watch. Whether it be movies, television shows, or music videos. But, I'm not so clear as to what is considered "inappropriate." Now, sexual content, extreme violence, and bad language is not something I want them to see, but is there a limit to the maturity of a movie which a child can watch?