UNIQUE'S RAR FILE LIBRARY
This library allows you to read files from RAR archives created with RAR and WinRAR. It supports decompression and decryption, and the library code is statically linked with your application (no external DLLs). Supported operating systems include Win32, SunOS and Linux.

UCL PORTABLE LOSSLESS COMPRESSION LIBRARY
UCL is a portable lossless data compression library. It is available in ANSI C source code form under the GNU GPL. The author claims that the decompression is simple, extremely fast and requires no memory. The decompression code can be squeezed into 200 bytes of code. It looks like it is a good candidate if you are writing applications that must execute in tight memory conditions, and don't mind releasing the source code for your application (which is required by the GNU General Public License).

BZIP2 LOSSLESS COMPRESSION LIBRARY
Bzip2 is a portable, patent-free, lossless data compression program and library (libbzip2). The author claims that it runs on "practically every (32bit/64bit) platform in the known universe" (including of course Linux and Windows). It is based on the Burrows-Wheeler transform and comes with a BSD-style licence. Full source code is available, along with pre-compiled binaries for a number of operating systems.

ZLIB
This is an excellent free C library that allows you to compress/decompress any buffer or file using the inflate/deflate method used by PKZIP, InfoZIP and others. As far as I can tell, you can use the code in the library freely in your programs without paying a cent in royalties. The library is apparently used in the Java archiver, jar. You can use this library on a large number of systems, including Win16, Win32, Linux, Unix, MSDOS, etc.

FREEWARE ZIP COMPONENT
Available at this site are DLL's, VCL's, examples and full source code for Borland's C++ Builder and Delphi that allows you to make PKZIP compatible ZIP archives from within your application. The source code is also available.

DJVU
An image compression library with source code from AT&T released under the AT&T Source Code License. Besides a portable thread library, the complete source for a decoder, and "a big piece of the encoder" together with other utilities are also available. Precompiled binaries can be found for Linux, Windows and various Unices.

LZO
A compression library with source code released under the GNU General Public License. Its purported advantage over zlib (see elsewhere on this page) is that it is fast and has a small memory footprint. An even smaller memory footprint version, called miniLZO is also available, allowing you to include compression in your applications at the cost of a very small increase in executable size (about 6kb on an i386, according to the website).

LHALIB
This library, which comes with source code, allows you to extract files that have been compressed with the free compression utility LHA. I think the library can be used in your programs royalty-free. It can be used on Win32 systems.