The GIMP (GNU Image Manipulation Program) is the closest thing to a free, open source alternative to Adobe Photoshop.
Unfortunately, while it rivals Photoshop in power and functionality (even offering some functionality Photoshop can't match), it is seriously deficient in terms of ease-of-use (both for novice and expert users).
The GIMP is available for Windows and Mac OS X as a native application, but this version tends to trail the X11 version in functionality and stability, which also makes it harder to install (and even less "native").