The GIMP is a GPL image retouch application. According to its homepage, GIMP "can be used as a simple paint program, a expert quality photo retouching program, an online batch processing system, a mass production image renderer, a image format converter", and for many other purposes. You may be interested in screenshots.
It was originally developed on X11 by two students, Peter Mattis and Spencer Kimball, who wanted a graphical editing program. It has since not only become a serious graphical editor for such tasks as photo retouching, image composition and image authoring with Ports to Windows (GIMP/Win32) and MacOSX (MacGIMP, which costs £10), but has also forked off the GimpToolKit, the most successful GUI ToolKit on Linux and other Unixoid systems.
TheGIMP's user interface is a very powerful, non-MDI design. WellUsedRhetoric says that AdobePhotoshop users will find it difficult to get to grips with the interface -- it suffers from the inevitable "It's almost, but not quite, entirely like AdobePhotoshop" complaints. There is an entire page devoted to this topic at GimpVersusPhotoshop. The interface will let you be extremely productive once you get to know it. Don't be put off by first impressions -- read a book, or post a question if you need help. For those of you who actually find the unique interface intuitive and productive, or just want to learn more, there's The GIMP User Group. The curious can visit a gallery of GIMP artwork.
A subproject originally called !FilmGimp? and now named CinePaint, which is based on a very old fork of TheGIMP's source code, is used in the film industry and has made its way onto Hollywood movies such as 2 Fast 2 Furious, Scooby-Doo, Harry Potter and Stuart Little. It is not a solution for the average home user's video editing needs though.