Bzip2 is a freely available, patent free (see below), high-quality data compressor. It typically compresses files to within 10 to 15 percent of the best available techniques (the PPM family of statistical compressors), while being around twice as fast at compression and six times faster at decompression.
Because it compresses well, it packs more into your overfull disk drives, distribution CDs, backup tapes, USB sticks, etc. And/or it reduces your customer download times, long distance network traffic, etc. It's not the world's fastest compressor, but it's still fast enough to be very useful.
Because it's open-source (BSD-style license), and, as far as I know, patent-free. (To the best of my knowledge. I can't afford to do a full patent search, so I can't guarantee this. Caveat emptor). So you can use it for whatever you like. Naturally, the source code is part of the distribution.
Because it supports (limited) recovery from media errors. If you are trying to restore compressed data from a backup tape or disk, and that data contains some errors, bzip2 may still be able to decompress those parts of the file which are undamaged.
Because you already know how to use it. bzip2's command line flags are similar to those of GNU Gzip, so if you know how to use gzip, you know how to use bzip2.
Because it's very portable. It should run on any 32 or 64-bit machine with an ANSI C compiler. The distribution should compile unmodified on Unix and Win32 systems. Earlier versions have been ported with little difficulty to a large number of weird and wonderful systems.