I'm pretty sure you can get a more formal copyright paper if you file it. However, it doesn't matter and you could even do it after the fact if someone infringes your copyright.
Registering your copyright entitles you to damages in court. It's quite valuable.
Edit: to be clear, with an unregistered copyright, you can still sue for an injunction to stop someone from distributing your material. You won't get your statutory damages, though.
http://www.copyright.gov/eco/