The beauty of Linux Distribution is that it can be customized to do almost anything you want. As long as you have the time and the desire to do it. Many popular Linux Distributions today was a result of individuals or group of people who were dissatisfied with the current options available. Lets look at some of those more popular special purpose Linux distributions out there.
1Parted Magic OS is a disk partition/repair distribution that supports more than a dozen file-systems and utilities to “Move, copy, create, delete, expand & shrink hard drive partitions. Clone your hard drive, to create a full backup. Test hard drives for impending failure. Test memory for bad sectors. Benchmark your computer for a performance rating. Securely erase your entire hard drive, wiping it clean from all data. Gives access to non-booting systems allowing you to rescue important data.”
2SystemRescueCd is similar to Parted Magic but it goes a few steps further and allows to repair and recover a system after it crashes. Sys-admin tools include file recovering, antivirus/rootkit scanner, resetting windows admin password, compressing and backing up existing system (to name a few).
3BackTrack Linux is a penetration testing distribution that tests network/computer security using different type of tools including: Information gathering, Vulnerability assessment, Exploitation tools, Privilege escalation, Maintaining access, Reverse engineering, RFID tools, Stress testing, Forensics, Reporting tools.
4Ubuntu Studio is an Ubuntu based distro catered towards creative people to create art. Contains popular Linux apps to edit and compose Audio, video, video, photography, graphics and publishing.
5Mythbuntu is an Ubuntu based PVR system using mythTV as a front-end. Can be used as an open-source alternative to Tivo and similar to ArchLinux based LinHES.
6Scientific Linux is based on Red Hat Enterprise Linux and a collaboration between Fermi National Accelerator Laboratory and the European Organization for Nuclear Research (CERN). As the name suggest, the distribution is geared towards scientists doing scientific stuff (I wouldn’t know).
7Tails A devian based live distro includes Tor, crypto and secure deletion tools for the paranoidamong us.
8LinuxCNC is a software system for computer control of machines such as milling machines, lathes, plasma cutters, cutting machines, robots, hexapods.
9Edubuntu is an Ubuntu based grassroot movement to make free education related software available to schools all over the world.
10VortexBox A Fedora based distro can be used as a music server/jukebox. It can rip CDs to FLAC and MP3 files, ID3 tag the files , and download the cover art. Vortexbox will then serve the files to network media players such as Logitech Squeezebox, Sonos, or Linn. The music files can also be streamed to a Windows or Mac OSX system.
One thing to note that how many of them are based on Ubuntu, which itself is based on Debian, probably due to how easy it is to create your own distro. This is far from an exhaustive list. There are hundreds if not thousands of Linux distributions out there. Feel free to share any unique special purpose distributions, in your comments.