I like to tinker with and teach computer graphics (check out my gallery), and there are lots of excellent free programs out there to work with.
My favourites are:
Blender (free & open source): 3D content creation suite.
Inkscape (free & open source): easy to use, 2D vector graphics program (similar to Adobe Illustrator or CorelDraw). I like the floss manual for inkscape.
Sculptris (free, closed source proprietary software): is an easy to use 3D sculpting program. It even comes with a pretty good PDF user manual (check your installation directory)
GIMP (free & open source): raster image editor (like Photoshop)
MyPaint (free & open source): digital painting program
Krita (free & open source): digital sketching & painting program
Many of these programs can be run as Portable Apps directly from a USB flash drive.
Some other good tools I keep an eye on (but admittedly haven't used a lot) are:
Fotografix (free): Light weight raster image editor
Alchemy (free & open source): Artistic brainstorming and concept development tool. It helps you create interesting shapes and patterns to use as inspiration for other artwork (kind of like cloud watching)
MakeHuman (free & open source): is a utility for generating realistic human models by tweaking parameters (like gender, age, height, muscle tone, etc.)
Terragen (free and commercial versions): is a powerful tool for generating realistic natural landscapes and environments.