Check out these screenwriting contests and don't forget to subscribe to the Script Angel blog to receive regular updates to this list:
Writers' Couch (Cascade Pictures) - Deadline: ongoing - Screenplay 80-140pp. UK residents and unrepresented writers only.
Sir Peter Ustinov Television Scriptwriting Award - Deadline: 1 July 2013 - Submit 30-60 minute television drama script. Applicants must be under 30 and non-US residents.
Screencraft Comedy Script Contest - Deadline: 1 July 2013 (early) / 1 October 2013 (late) - Feature screenplays up to 140pp.
Screenplay Festival - Deadline: 1 July 2013 (regular) / 1 September 2013 (late). Feature length screenplays and teleplays over 60pp (no max).
Slamdance Writing Competition -  Deadline: 2 July 2013 - TV pilots up to 80pp, feature screenplays 90-150pp.
New Hampshire Film Festival Screenplay Contest - Deadline: 5 July 2013 (regular) / 15 July 2013 (late)
Tracking B Feature Script Contest - Deadline: 28 July 2013 (early) / 1 September 2013 (regular) / 27 October 2013 (late)
Big Break Screenwriting Contest - Deadline: 31 July 2013 (extended). Teleplays 25-70pp / Screenplays 80-120pp.
John Brabourne Awards - Deadline: 31 July 2013. Financial support to up and coming talent who may have suffered set-backs. UK residents only.
American Zoetrope Screenplay Contest - Deadline: usually 1 August 2013 (Early) / 6 September 2013 (Final) -  Screenplays 82-145pp.
Script Hot House from Write2Screen - Deadline: 2 August 2013. UK residents only. Successful applicants receive script development programme.
Fresh Voices Screenplay Competition - Deadline: 14 August 2013 (early) / 10 September 2013 (regular) / 9 October 2013 (late) / 7 November 2013 (final)
Underwire Film Festival Short Script Competition - Deadline: 16 August 2013. Short film scripts only. Female screenwriters only. Entrants must be British or residing in the UK.
BAFTA Rocliffe New Writing Forum: November Forum  - Deadline: 20 August 2013 (early) / 20 September (regular)
Blue Cat Screenplay Competition - Deadline:  1 September 2013 (Early) / 15 October 2013 (Regular) / 15 November 2013 (Late). Accepting shorts and feature length scripts.
One In Ten Screenplay Contest - Deadline: 1 September 2013. Screenplays 90-125pp. Must feature at least one primary character who is gay, lesbian, bisexual or transgender.
The Writers Place Screenplay Contest - Deadline: 15 September 2013 - Feature length scripts up to 130pp, teleplays/short script up to 45pp.
London Independent Film Festival Screenplay Contest - Deadline: 30 November 2013 (regular) / 1 March 2014 - short & feature length scripts.
To look out for at a later date:
The Red Planet Prize - Deadline: usually May
Coming Up 2014 (Channel4 & Touchpaper Television)  - Deadline: usually July
Berlinale Talent Campus (Script Station) - Deadline: usually September - opens for applications July 2013
BBC Writersroom Script Call - Deadline: usually Autumn
Guiding Lights Mentoring Scheme - Deadline: usually October
The Launch Pad Competition (Tracking Board) - Deadline: usually November
4Screenwriting (Channel Four) - Deadline: usually November (opens September 2013)
Cinequest Screenwriting Competition  - Deadline: usually November
L.A Comedy Shorts Screenplay Competition - Deadline: usually January - categories for short film script, feature film script and tv sitcom pilot script.
Writers Revolution Screenplay Competition - Deadline: usually January
Cinestory Screenwriting Contest - Deadline: usually February - Screenplay 85-130pages.
Mediterranean Film Institute Script2Film Workshop - supported by European Media Desk - Deadline: usually February.
United Film Festival Screenwriting Contest - Deadline: usually February - Drama or Comedy or Horror/Thriller as Short screenplay under 45pp or Feature screenplay over 45pp (no max).
Comedy Central/NYTVF Pilot Competition - Deadline: usually March - Sketch/narrative/single camera sitcom and animated comedy. USA residents only. Pilot script plus 4-11' pilot presentation DVD.
Scriptapalooza -  Deadline: usually March - Screenplays 80-140pp.
European Independent Film Festival Script Competition - Deadline: usually March - Short scripts 5-50pp & feature length scripts 80-130pp. Looking for scripts NOT aimed at mainstream Hollywood film markets.
Scriptwriter Contest from Overbrook Entertainment & ANA Alliance for Family Entertainment - Deadline: usually March - Comedy scripts 30" & Drama scripts 60". US residents only.
NBC/NYTVF Drama Challenge - Deadline: usually March. Looking for original tv drama series. Submit series overview, pilot script & produced pilot scene.
Film Bazaar India Screenwriters Lab - Deadline: usually March. Applicants must be Indian passport holders.
BAFTA Rocliffe New Writing Forum: TV Drama May Forum - Deadline: usually March - Single dramas, mini-series, comedy drama and continuing drama.
Sitcom Mission - Deadline: usually March - Submit 15 minute sitcom script for tv, radio or stage.  Aimed at UK residents.
The Sitcom Trials: So You Think You Write Funny? - Deadline: usually March- Submit 10 minute sitcom script for tv, radio or stage. Aimed at UK residents.
The PAGE International Screenwriting Awards - Deadline: usually April - Short scripts up to 40pp, feature screenplays 80-120pp, TV drama pilots 50-70pp, TV comedy pilots 25-45pp.
Big Bear Screenwriting Competition - Deadline:  usually April -Screenplays 90-130pp.
Beijing International Screenwriting Competition - Deadline: usually April - Submit proposal for feature film, which must prominently feature Beijing as location. Open to anyone living in US.
Maison des Scenaristes - Deadline: usually April - Submit synopsis & first 5 pages of feature film (English or French language) project to win chance to pitch to producers at Cannes.
Edinburgh International Film Festival Talent Lab - Deadline: usually April. Open to screenwriters, producers & directors. Feature films only. Lab takes place June 2013.
Nick Darke Award - Deadline: usually April - Submit 750 word pitch for film, radio or stage play idea plus 20pp writing sample.
Sundance Screenwriters Lab - Deadline: usually May - Feature film scripts. US residents only.
Nicholl Fellowships in Screenwriting - Deadline: usually May - Screenplays 90-120pp.
Script Pipeline Screenwriting Contest - Deadline: usually May - Feature length screenplays.
Script Pipeline TV Writing Contest - Deadline: usually May - Any length script, pilot of original or spec of existing show.
Screenwriting Goldmine Competition  - Deadline: usually May - Film & TV scripts 45-120pp.
Save Our Scripts - Deadline: usually May - Pitch for project to be developed plus sample of previous work (feature script or two short film scripts).
Disney/ABC Writing Fellowship - Deadline: usually May. Applicants must be able to prove US employment eligibility.
Austin Film Festival Screenplay & Teleplay Competition - Deadline: deadline usually June - Feature scripts 90-120pp, teleplays (original pilot or spec of existing show) 45-70pp, sitcom scripts 22-40pp. NOW IN ASSOCIATION WITH AMC.
Screamcraft Horror Script Contest - Deadline: usually June - Feature screenplays up to 140pp in Horror genre.
Warner Bros' Writers' Workshop - Deadline: usually June (submissions usually accepted from 1 May). Submit writing sample for one of their listed current shows. Successful applicants must be able to attend regular workshops in LA.
Fox-NYTVF Comedy Script Contest - Deadline: usually June (submissions usually accepted from 1 May). TV scripts 25-35pp. US residents only.
The Quest Initiative - Deadline: usually June. Submit logline only.
NYC Midnight Screenwriting Challenge - Deadline: usually June - Short screenplays based on assigned criteria.
Shoreline Scripts Feature Screenplay Competition - Deadline: usually June - Feature screenplays 80-120pp, short screenplays 3-20pp.
Just Effing Entertain Me Screenwriting Competition - Deadline: usually June - Screenplays 90-120pp.
Rawi Screenwriters Lab (the Royal Film Commission, Jordan) - Deadline: usually June. Arab screenwriters only.
Good luck!