GIMP is the GNU Image Manipulation Program. It is a freely distributed piece of software suitable for such tasks as photo retouching, image composition and image authoring. It can be used as a simple paint program, an expert quality photo retouching program, an online batch processing system, a mass production image renderer, a image format converter, etc.
Tux Paint is a simple and entertaining drawing program geared towards young children. It has a simple interface, sound effects, and a cartoon character (Tux, the Linux penguin). Along with drawing brush strokes, lines and shapes, you can also enter text and place "rubber stamp" (or "sticker") images on the picture. Tux Paint is extensible, and could be useful in an educational environment (such as a grammar, elementary, or grade school). It's portable across numerous platforms, and runs well even on slower systems like the Pentium 133MHz.
Allegro Sprite Editor (ASE) is a program specially designed with facilities to create animated sprites that can be used in some video game. It lets you create static images, characters with movement, textures, patterns, backgrounds, logos, color palettes, etc. It focuses on pixel editing to do pixel art. It isn't a photo retouching tool or a vector graphics editor. Mainly, it is a tool to create tiny animations pixel-by-pixel.
FrAid (Fr[actal] Aid) is a programming language that is appropriate for mathematical computations, visualization, batch processing, and more. It features both a standalone application that provides a programming environment for the language and a system for integrating the language with Java. The Java interface allows mathematical equations and formulas to be used with Java code, making it easier to process numerical computations, symbolic computations, imaging, CAD, and more.
Arachne is program that implements Avidan and Shamir's seam carving technique for content-aware image resizing. It allows realtime, fluid image resizing using this fascinating technique. Seam carving works by removing the "boring bits" from an image, so it can change the aspect ratio of many images without changing the shape of the objects inside.