Adobe Photoshop is a fantastic software product. I use it at CNET every single day. However, I don't own a personal version at home, and I find that I don't miss it much for my own limited image editing and graphic design needs. For cropping snapshots, removing red-eye, resizing, or creating LOLcat images, I turn to the free image editors available at CNET Download.com.
The grandaddy of free design software is the GIMP (short for GNU Image Manipulation Program), which provides much of the functionality of Photoshop, with a very large and dedicated community that produces tons of valuable tutorials. However, the GIMP isn't the most user-friendly application. Newbies would be advised to try GIMPshop, which puts a Photoshop-like interface on top of the GIMP's core functionality.
Personally, I use several different applications, but the one I return to most is the fabulous freeware Paint.NET. It requires the .NET framework (also free) from Microsoft, but once installed it will handle all of your basic image-manipulation desires. A tabbed interface, unlimited undo history, and powerful layer tools are some of the major highlights.
For viewing images, all of my JPEGs, GIFs, BMPs, and the rest are associated with the free little application IrfanView. It's not just for browsing, however, as later updates added basic image-editing functions. Another favorite with a few CNET staffers is the top-rated freeware FastStone Image Viewer. It's not as light as IrfanView, but the image-editing features are more integrated.
So what fantastic free image-editing software application did I miss? Which program is your favorite image editor, regardless of cost? Tell me about it in the commments.