I don't use photoshop, and when someone asks for a free alternative in DA, I suggest the GIMP. The interface takes getting used to (I personally hate it), but it does do what most commercial programs can do. That, plus it has a lot of support (tutorials, brushes, etc) from the DA community, far more than other free photomanipulation programs. There's also "GIMP shop", a modified version of GIMP to look like photoshop (in case you're already used to photoshop or plan to get photoshop in the future).
http://www.gimp.org/
There _are_ major differences, such as GIMP being incapable of CMKY (only relevant if you're making commercial prints), or differences in their magic lasso (annoying, but unless you've already had a lot of experience with PS it shouldn't be that big a problem), but generally GIMP is very well considered a solid alternative to PS.
There also paint.net, pixia, and dogwaffle (haven't used them before, so can't comment)
http://www.getpaint.net/index.html
http://park18.wakwak.com/~pixia/index.html
http://www.thebest3d.com/dogwaffle/free/
If you're looking for a paint progam (a program that emulates traditional media, as opposed to a pure raster graphics editor), I recommend Artweaver, which does the job and is (realtively) easy to use (can't figure out how to use layers yet, though)
http://artweaver.en.softonic.com/
For vectors, there's inkscape (buggy, very buggy, but gets the job done when it does work):
http://www.inkscape.org/
Of course, feel free to ignore all of the above if you choose to get PS (bought or otherwise) anyway. The above are just free alternatives.