You can always try anything linked to big name products like Final Draft. The developers of Final Draft hold their own annual screenwriting competition. Information can be found at:
http://www.finaldraft.com/index.phpOr you can try out the American Zoetrope Screenplay Contest which is hosted by, you guessed it, American Zoetrope. If you don't know who that is, it's owned and operated by none other than film legend Francis Ford Coppola.
http://www.zoetrope.com/contests/Check them out and see what you think. Of course, there are a ton of contests out there and some are better suited than others. If you're writing for a specific genre you may even want to do a search for contests in that particular realm story telling.
Have fun!
Ryan
