What I am currently reading: The Writer
Contests are a great way to give yourself a self-imposed deadline, a chance to write with a goal in mind and of course a way to hone your writing skills. Then there are the prizes...Those are always a big draw. Some give away money, others reward with publication and some even fly you out to some fun destination to receive your award in person. If there is one down side, I would say it is the money you have to spend to enter. Most contests (but not all) have an entry fee. It isn't usually a lot of money, so I find it worth it for the chance at the bigger prize.
Look at the guidelines carefully and make sure you are not giving away all your rights to any of your work. There is a great article by the Science Fiction & Fantasy Writers of America about what to watch out for with a contest. Read the article, but don't let it scare you off, because most contests are legitimate.
Here are some great links with lists of upcoming writing contests.
fundsforwriters.com (scroll down on the page)
Good luck! Let me know when you win.
Happy contest writing!