1. Go to folder <Documents>\My Games\Borderlands\WillowGame\Config
  2. Open WillowEngine.ini
  3. Search for "FullScreenMovie"
  4. Erase all entries in the [FullScreenMovie] section. Don't erase anything in the next section, which starts with a line wrapped in square brackets.
  5. Make the file read-only. (Right click on it, choose Properties, then check Read-only.

This skips the 2K, Gearbox, and NVidia movies. The copyright, gamespy and autosave are hard coded in and will still show up.