Gimp – Very powerful image manipulation program, great for photo retouching and image creation. There are other downloads, GTK and runtime environment for this program to work properly. This program currently runs on Linux, Windows (XP and Vista), Mac OSX, and some Unix based systems.
Ultimate Paint – Image creation and manipulation program for Windows systems. This is a pretty compact and fast running graphics program with plenty of features.
Skencil – An interactive vector drawing program for Unix and Linux operating systems built on the Python language. This program has tons of features like gradient fills, bezier curves and you can bend text along paths to name a few.
Pixia - Originally a Japanese only edition, Pixia is a very nice paint tool with full layers support and many other features. The English version website does lack information and support so you will likely need to search the web for information on learning to use this tool. This is currently a Windows only program and does support some drawing tablets.
InkScape – If you have been looking the free answer to Adobe Illustrator or CorelDraw, IncScape is a great alternative. This is a full featured vector graphics editor. The website has a tons of information, tutorials and galleries of work created with the program, to give you a good idea of what you are getting involved with.
Paint.net – A free image and photo editing software for Windows based PC's. This program was voted #19 out of the top 100 programs of 2007 by PC World. It has full support for layers and special effects, the tools are top notch and highly recommended by many users. There is a strong online community for support and frequent updates to the software. Comparable to Adobe Photoshop.
SmoothDraw NX – A freehand drawing tool designed for use with tablets. Several choices of brushes and pencil strokes for creating realistic drawings. Also auto smoothes lines if you are using a mouse to draw with.
ImageForge – An image editing and creation program for Windows systems. Although this program is a little rougher than some of the others it still has some nice features like easily creating 3D text, red-eye removal and you can easily create your own Windows screen savers.
Brush Strokes – Free graphics editor, with support for many of the popular and common image formats. It isn't as full featured as some of the other programs but it is a good choice for less technical or light users.
Project Dogwaffle – A painting and drawing program developed for the PC. Has a nice set of tools and very functional, although does lack features of some large programs.
Sodipodi – This is a vector based drawing program that operates on most Unix and Windows systems. It has a ton of features like out of center gradients, patterned lines, dynamic xml editor and you can easily create vertical text.
Karbon14 – Another nice, full featured vector based drawing program released under the GNU license. This program comes as part of the Koffice project which includes a whole suite of tools in KDE.
ArtWeaver – A freeware paint and drawing program for Windows designed to simulate natural brush tools and effects for artists used to working on canvas. It supports most common file formats, has the standard editing tools like found in many popular graphics programs and offers a few effects filters.
GimpShopdotnet – This is a modified version of Gimp, designed to work and feel more like Adobe Photoshop, allowing Photoshop users a comfortable free alternative.
ImageMagick – A nice command line program for editing and creating images. There are a whole bunch of useful features like shearing and transforming images, flip, mirror and rotate images and a whole lot more.