Forrest Gump
It's a story about a man from the American south who is mentally handicapped. It shows him growing up and going through many important events of the 1960s and 1970s in the United States, including civil rights movements, watergate, the Vietnam war, peace movements, as well as many other American icons and cultural movements along the way.
It's a really great story. It shows a complicated world through the eyes of a man with an innocent mind. The main character, Forrest, and several other important characters are southern, so they speak with a southern accent. However, they generally speak fairly slowly, so even if you aren't used to hearing one you can probably still understand what they're saying. The movie was made in 1994, not terribly recent, but not old either. If you're interested in American culture, I definetly recommend it!