<p>In honor of the <a href="http://prize.hutter1.net/" rel="noreferrer">Hutter Prize</a>, 
what are the top algorithms (and a quick description of each) for text compression?</p>

<p>Note: The intent of this question is to get a description of compression algorithms, not of compression programs.</p>

There's always
lzip
.
All kidding aside:
Where compatibility is a concern, PKZIP (
```
DEFLATE
```
algorithm) still wins.
bzip2 is the best compromise between being enjoying a relatively broad install base and a rather good compression ratio, but requires a separate archiver.
7-Zip
(
```
LZMA
```
algorithm) compresses very well and is available for under the LGPL. Few operating systems ship with built-in support, however.
rzip
is a variant of bzip2 that in my opinion deserves more attention. It could be particularly interesting for huge log files that need long-term archiving. It also requires a separate archiver.