Image Viewers & Editors
These are predominantly image viewers. They may have basic editing capabilities, but are not full-brown graphics-editing/creation software.
Ristretto is part of the xfce project, made to be fast and lightweight. It can display and rotate images and run a slideshow.
EyeOfGnome, a comparatively simply application, is strictly an image viewer and has no image editing capabilities.
Geeqie is a fast and lightweight image viewer without image editing. It can, however, edit image metadata.
ImageMagick is a very versatile application that is meant mostly to run from CLI, but can display and manipulate images in the GUI as well. It can be used to make a montage, convert image formats and make animated GIFs, among many other things.
These are photo organizers that allow you to import and organize photos within the application using folders, tagging and other capabilities.
gthumb is somewhere in-between an advanced image viewer and a basic photo organizer. it also has image editing and gallery export.
KPhotoAlbum is built around the idea of annotating your photos and being able to quickly find photos based on various criteria.
digiKam is an advanced application with a plug-in architecture for extending its capabilities. It can even import photos from social networking sites.
F-Spot is a photo management application with built-in photo editing capability. It can generate photo galleries and make picture CDs, among other things.
Shotwell has replaced F-Spot as the default GNOME photo management application. It can import photos directly from a camera and has basic photo editing features as well.
Image Creation & Editing
GIMP, the GNU Image Manipulation Program, is the undisputed king of image editing and creating on GNU/Linux. It is what Photoshop is to other platforms, except its absolutely free, in every way. It also runs on all major platforms, so you're not locked into any particular one.
Pinta, on the other end of the spectrum, is meant to be a very simple to use graphic editor, much like Microsoft Paint, but has more features and customization options.
Krita is a painting and illustration application and is aimed at cartoonists, illustrators and concept artists.
Inkscape is a vector drawing application that's available for all major platforms.
MyPaint is a bitmap/raster graphics editor available for all major platforms. It can be used with pressure-sensitive tablets.