Contests to consider:

Nicholl Fellowships in Screenwriting

The Austin Film Festival

PAGE International Screenwriting Awards

American Zoetrope

Creative World Awards

Script Pipeline

Scriptapalooza

Horror Contests:

Shriekfest

Screamfest LA
Make sure you research a contest before entering. 
Do your homework before emptying your wallet.
Those I've listed above have a good track record.