Most creative professionals, when asked what piece of software they use most, will most likely say Adobe suite of applications. But for students and non-professionals, Adobe’s pricetags can be quite intimidating. Luckily, there are a few free/cheap alternatives.
Most prominent is the GIMP, a powerful and totally free, open source alternative to Photoshop that is available for Windows, Linux, and Mac OS X:

If you find the GIMP intimidating, another open source image editing program, based on the GIMP is available called Seashore, which is available only for Mac OS X:

Finally, Wouldja Draw is a simple vector drawing application for Mac OS X. It’s not free, and looks rather limited in its functionality, but at $29.95 (there is a free demo) it sure beats the $500 sticker price of Adobe Illustrator if you only need to create the occasional simple vector images:

UPDATE:
Readers in the comments section point out some other free/cheap alternatives:
Inkscape is a free vector graphic program that works on Windows, Mac OS X, and Linux. Xara is a competetively-priced alternative as well (for Windows).