The Director/Composer

Many directors are multi-faceted - with cinematography, writing and editing also in their credits.  Composing the film's score is also one talent that several composers use.  For most, they compose music for their own films, with a few composing for other directors.  

The reason why I do not work with professional composers any more is that I get too many musical ideas of my own, and composers, understandably enough, resent being guided too much - Satyajit Ray

Here are 12 directors that took up the task of composing.  For each, you'll find a short list of films they've directed as well as the scores they have written.

Clint Eastwood
As Director: The Outlaw Josey Wales (1976), Pale Rider (1985), Unforgiven (1992), Mystic River (2003), Million Dollar Baby (2004), American Sniper (2014)
As Composer: Mystic River (2003), Million Dollar Baby (2004), Flags of our Fathers (2006), Hereafter (2010)
(Golden Globe nominee: Best Original Score - Million Dollar Baby, Grace is Gone, Changeling)

Charlie Chaplin
As Director: The Gold Rush (1925), City Lights (1931), Modern Times (1936), The Great Dictator (1940), Limelight (1952)
As Composer: The Gold Rush [1942 edition] (1925), City Lights (1931), Modern Times (1936), Limelight (1952)
(Oscar winner: Best Original Dramatic Score - Limelight.  Won in 1973)

John Carpenter
As Director: Assault on Precinct 13 (1974), Halloween (1978), The Fog (1980), Escape from New York (1981), The Thing (1982)
As Composer: Assault on Precinct 13 (1974), Halloween (1978), The Fog (1980), Escape from New York (1981), Big Trouble in Little China (1986)

Robert Rodriguez
As Director: Desperado (1995), From Dusk Till Dawn (1996), Spy Kids (2001), Sin City (2005), Machete (2010)
As Composer: Spy Kids 1-4, Sin City (2005), Kill Bill Vol 2 (2004), Planet Terror (2007)

Tom Tykwer
As Director: Run Lola Run (1998), Perfume: The Story of a Murderer (2006), The International (2009), Cloud Atlas (2012)
As Composer: Run Lola Run (1998), Perfume: The Story of a Murderer (2006), The International (2009), Cloud Atlas (2012) [all composed with Reinhold Heil, Johnny Klimek]

Satyajit Ray
As Director: Apu Trilogy (1955-1959), The Music Room (1958), Charulata (1964)
As Composer: Shakespeare-Wallah (1965), Baska Badal (1970), The Golden Fortress (1974), The Home and the World (1984)

Trey Parker
As Director: Cannibal! The Musical, South Park: Bigger Longer & Uncut, Team America World Police
As Composer: Cannibal! The Musical, South Park (TV), South Park: Bigger Longer & Uncut, Team America World Police
(Oscar nominee: Best Song - Blame Canada)

Dario Argento
As Director: Bird with the Crystal Plumage (1970), Deep Red (1975), Suspiria (1977)
As Composer: Suspiria (1977), Dawn of the Dead (1978)

Anthony Hopkins
As Director: August (1996), Slipstream (2007)
As Composer: August (1996), Slipstream (2007)

John Ottman
As Director: Urban Legends: Final Cut (1999)
As Editor: The Usual Suspects (1996), X-Men 2 (2003), Superman Returns (2006) , X-Men Days of Future Past (2014)
As Composer: The Usual Suspects (1996), X-Men 2 (2003), Fantastic Four (2005), Superman Returns (2006), Astro Boy (2009), Jack the Giant Slayer (2013)

Benh Zeitlin
As Director/Writer: Beasts of the Southern Wild (2012)
As Composer: Beasts of the Southern Wild (2012) [with Dan Romer]

David Lynch
As Director: Eraserhead (1977), The Elephant Man (1980), Dune (1984), Blue Velvet (1986), Mulholland Drive (1997)
As Composer: Eraserhead (1977)
Additional Music: Blue Velvet (1986), Lost Highway (1977), Mulholland Drive (1997)