I bought the Writer's Market book a few days ago. Looking through it there are two contests that close at the end of the month.

L. Ron Hubbard's - Writers of the Future www.writersofthefuture.com

and

Glimmer Train - http://www.glimmertrain.com/

The first is for new writers and Glimmer Train has an open contest and one for new writers. New writers are ones who have not sold anything or just a few stories. You'll have to read the rules. Glimmer train cost $12 and Writers of the Future is free.

Dave K