The Disney/ABC Writing Program is currently accepting submissions and applications. The submission period is May 1 through June 1.
The Warner Bros. Writers' Workshop is accepting submissions beginning tomorrow through June 1.
The Screenwriting Expo Screenwriting Competition is currently open to entries. Final deadline is July 10. They have categories for feature, teleplay and short. The Screenwriting Expo itself will take place September 15-18 at the Westin Los Angeles Airport Hotel.