Question: I was just wondering, what's the difference between these file formats? Shouldn't there be just one or two that generally tend to perform superior to most others?

Answer: 
[`compress`](http://en.wikipedia.org/wiki/Compress) (the Unix command, ported to Linux and others) itself only has one file extension that is used for its output, and that is `.z`

There are other compression algorithms (and their associated programs) that compress files differently for different results.

Some popular programs include:

* [Gzip](http://en.wikipedia.org/wiki/Gzip) which has the extension `.gz`
* [Bzip](http://en.wikipedia.org/wiki/Bzip2) which has the extension `.bz2`
* [Rar](http://en.wikipedia.org/wiki/Rar) which has the extension `.rar`
* [Zip](http://en.wikipedia.org/wiki/ZIP_%28file_format%29) which has the extension `.zip`
* [7-zip](http://en.wikipedia.org/wiki/7z) which has the extension `.7z`
* and many more...

Generally newer archivers will use better compression algorithms, usually at the cost of taking longer (requiring more CPU time) to compress or requiring more memory or both. 

As a general rule though, the newer the program, the newer it's algorithms and therefore the better its compression will be. `compress` is as old as the hills and its compression ratios tend to be a lot worse than more modern programs like 7-zip.
I prefer compressing my data using \*.rar with WinRAR as it is completely customizable. I use it because I can choose how much I want to compress it and I can set passwords to protect my archive. If I'm doing something involving disk images, I'll compress to \*.iso or \*.daa using PowerISO. 

Whenever I'm not on one of my own computers, I compress it using Windows 7's built-in \*.zip compressor. On Ubuntu, I will probably compress in \*.tar.gz or \*.zip.