The GIMP (GNU Image Manipulation Program) is a powerful photo and image processing program, similar in many ways to Adobe Photoshop, but lacking the CMYK support (though that is being remedied) and many of the plugins that professional graphic artists will demand (especially those who deal with print).
Its multi-window interface seems quite controversial, yet Photoshop on the Mac uses a similar interface.
The program should do everything the average user will want, and a lot more besides. In fact, it may be more powerful than many need, and the program has a steep learning curve.
Training Resources / Tutorials
Here are a list of helpful tutorials for the Gimp: