To the best of my knowledge almost any film festival will accept films from anyone but there are fests geared for kids.
Kids First put on one of the bigger ones.

Lots of regional fests are popping up as well. In seattle Bumpershoot is starting to include more kids films in the film fest part.

As for something that is strictly a contest there are many around. Each year the ACM has awards - but they are tied to local PEG centers. if your project has aired on, or been made for, Community Access than it would be elegible. No age limits on that. One of the best concepts, IMO, is something put on by Scenerios USA. But there are some problems getting into it - it is a mainly a school based program and right now there are really only 3 schools in America that are part of it. Sad, but true. But if you can get your loacl school or teacher, at the least, to get involved than you have a better chance. it starts off with a script as part of the "What's the Deal?" contest. The script gets sent around and voted on and the ones that get selected get made into shorts. And the other "catch", which if you are serious about film making as a teen shouldn't even be considered a "catch", is that you do not direct the film, just co-direct. But the "other" director is a "Hollywood" director. People like Griffin Dunne and Michael Apted for example. (Actually it shouldn't even be thought of as a 'catch" for anyone who wants to direct - young or old.)