As a non-designer (and Linux user), GIMP and Inkscape have served me well for light graphic and vector editing. Paint.NET is another good option if you're using Windows.
Of course, none of these are going to be great for Adobe-specific formats (PSD, AI, etc.), but they're plenty capable pieces of software.
The best advice I can offer is to make friends with a graphic designer, then pass the buck on non-trivial design tasks. ;)
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