PNG - Portable Network Graphics
PNG is the new graphics format with lossless compression. It has support for most pixelformats, including alpha channel. It is also free to use.
Free jpg library.
Free open source image loading/saving programming library.
Free open source image saving/loading programming library.
squish - DXT Compression Library
Open source library under MIT license to perform DXT compression for images. Supports DXT1, DXT3, and DXT5.
Open Source and free implementation of the JPEG 2000 image standard.
SFML - Simple and Fast Multimedia Library
zlib open source, cross platform, light-weight library for doing various low and high level tasks: windowing, audio, input, networking, graphics, etc. SDK is based on separate classes so it's possible to use parts of the library if that's what's desired.
.werkkzeug 3 TE (texture edition)
A free tool for procedurally generating textures. The engine for generating the textures can be licensed for a rather steep price so that it can be embedded in applications.