The Exorcism of Emily Rose (2005; TYPO -- originally typed 1995. sorry for the confusion), PG-13.
One of the first (THE first?) movies to come from Act One, the latest and best-organized effort to get Christians into Hollywood to make mainstream (i.e., no "christian celebrities," no altar call moments, not designed for the Christian bookstore direct-to-video set) movies that tackle issues of faith.
I enjoyed this movie a lot -- the casting, design, script, effects were all top-notch. I am not a fan of horror films, and this one isn't really one, despite the name and the marketing of it when it was in theatres. First, it is a courtroom drama -- Emily died during the exorcism, and the priest is on trial; second, it is an inelligent debate on the role of the spiritual in the modern world; and third, a horror film. The flashbacks of Emily's possession and exorcism are intense and frightening, but not gory -- the only blood is Emily's stigmata.
Again, this is not a movie for the Church basement, but is an intelligent, fair and balanced movie that at the very least should be one that encourages discussion, maybe even debate.