Main Director who started with music video include:

David Fincher: Madonna - GlamDavid Leo Fincher (born August 28, 1962) is an American filmmaker and music video director, known for his dark and stylish thriller movies, such as Seven (1995), The Game (1997), Fight Club (1999), Panic Room (2002), and Zodiac (2007). He received an Academy Award nomination for Best Director for his 2008 film The Curious Case of Benjamin Button.

Spike Jonze: Fatboy Slim – Praise You
Spike Jonze (born Adam Spiegel; October 22, 1969) is an American director and producer, whose work includes music videos, commercials, film and television. He is best known for his collaborations with writer Charlie Kaufman, which include the 1999 film Being John Malkovich and the 2002 film Adaptation., and for his work as director of the 2009 film Where the Wild Things Are. He was also a co-creator and executive producer of MTV's Jackass.
  He is currently the creative director of VBS.tv. He is also part owner of skateboard company Girl Skateboards with riders Rick Howard and Mike Carroll.

Michael Gondry: Foo FightersMichel Gondry (born May 8, 1963) is a French film, commercial and music video director and an Academy Award-winning screenwriter. He is noted for his inventive visual style and manipulation of mise en scène.