GIMP is an excellent suggestion. It's the closest free program that you'll get to the mighty (but expensive) Photoshop. However you need to be aware that there's quite a steep learning curve involved with both of those programs. Anyone who attempts to use Photoshop without buying at least one good book about it is likely to struggle. Similarly, if you're going to use GIMP, I strongly recommend downloading (and really studying the documentation for it).
Picasa is far easier to use (but, of course, without all of the 'bells and whistles' that GIMP has). Serif PhotoPlus Starter Edition is also well worth a look. (It's a 'lite' version of Serif's full commercial program, which is much-praised):
http://www.serif.com/...g-software/php-se.asp
I'd agree with Chuck that Windows Movie Maker is probably good enough for most home movie-making. However Lightworks (which has long been a favourite tool of professional film makers) has recently been placed into the public domain. No other free video-editing program can come anywhere near to it:
http://lightworksbeta.com/
Chris