LZW (named after the inventors Lempel, Zif and Welch) is a compression algorithm used among other things in GIF, TIFF (when used with the corresponding options) and Unix' compress.
The algorithm is patented by the company UNISYS. In the mid-nineties, when the Internet took off and GIF became popular with web browser support, UNISYS began enforcing their patent, see http://www.unisys.com/about__unisys/lzw/ .
According to the interpretation of the LPF at http://lpf.ai.mit.edu/Patents/Gif/Gif.html the UNISYS patent will expire in June 2003 (IANAL, and sources on the 'net are not really reliable for legal advice either, so don't depend on this opinion).