The GIMP for Linux
This Open Source image editor packs a surprising amount of power, and is well-designed, if a bit eccentric in layout. Even though it's free, it compares favorably to the power of Photoshop, and includes many of the kinds of photo-editing tools that come with that program, including filters, effects, masks, layers, and more.
Of course there are the basics tools you'd expect in a photo editor, such as red eye removal, but there is plenty more here. If you're looking for professional-level photo editing, but don't want to spend a bundle--or even a penny--this is the program for you.
Note: This link takes you to the vendor's site, where you can download the version of the software that's correct for your Linux distribution.