Debian is a distribution that is well known for its emphasis on software freedom. All software included with Debian is free for use and modification by anyone. Debian also supports an impressive packaging system that allows automatic downloading and installation of software as well as automatic upgrading of every software package on the system.
Knoppix is a Linux distribution that is normally run completely from CD. An entire Linux system can be run directly from the CD, without ever installing to the hard disk. This allows users to learn and use Linux without having to resize existing partitions, while storing data on existing hard disk partitions.
Additionally, Knoppix can be installed to the hard disk. It is Debian-based, so the final installed version is very similar to use. Configuration after installation is faster than Debian thanks to Knoppix's fast detection of common hardware.
The Gentoo Linux distribution resembles Debian; it also sports an impressive software installation/update system and makes an effort to keep software free by not depending on any non-free software. Gentoo differs from Debian primarily in that it compiles all programs from source code on the computer it is running on. This allows software to be optimized for the specific computer, resulting in an increase in speed. However, it also makes software installation and updating slower. Gentoo packages are often more up-to-date than Debian packages, allowing users to run the latest software.
Slackware Linux is a distribution intended for users who intend to fully learn the internals of Linux/UNIX. While those who are new to Linux can certainly use Slackware, the learning curve is steep. While Slackware supports several package management systems, there is still an emphasis on manual package installation and manual system configuration.
OpenBSD is widely considered to be the most secure open source operating system in existence. It has had one remote system vulnerability in the last 7 years. Like FreeBSD, OpenBSD also sports maturity and stability; some speed sacrifices are made for security. OpenBSD also supports a source code-base package management system. OpenBSD has a very steep learning curve.
FreeBSD is not a Linux distribution; it is derived from the original UNIX source code. As such, it is much more mature, more stable and faster than Linux. It supports a source code-based package management system. FreeBSD may have a slightly steeper learning curve than Debian, Gentoo or Knoppix; it historically does not focus on attracting inexperienced users.