I am not a die-hard recipe contest entrant, but I've entered a few. I've never won anything, except for a bake-off at my daughter's school where I suspect that the total number of entrants was exceedingly low :) If you enjoy putting fresh twists on favorite recipes, you might try entering a few. You never know if you'll win, and the process of coming up with new dishes can be quite a lot of fun (especially if you have willing taste-testers around)
I would caution against anything that requires an entry fee, and make sure you read the rules carefully. For a lot of contests, the sponsor retains the right to publish your recipes later even if you don't win (potentially without paying or notifying you), so know what you're doing before you click that "submit" button.
Here are a few that I found recently. I have entered both the Pillsbury Bake-off and the Better Homes and Gardens contests in the past. Happy Baking!
Pillsbury Bake-Off The winning recipe earns $1 million. Hurry, recipes are due in April!
Better Homes and Gardens magazine This contest runs monthly in their magazine. The winners get cash and publication in the magazine.
Better Recipes seems to be run by Better Homes and Gardens. This site hosts a weekly theme contest and a yearly grand prize winner.
Cupcake Cup Photo Challenge This one looks like fun for bakers who are more aesthetically inclined than I am :)
The Perfect 3 from Cooking Channel. Looking for the "perfect recipe" in each of 13 different categories.