Exhaustive and up to date lists of distributions are available from distrowatch.com and lwn.net
Here is a shortlist of our preferred distributions:

• Ubuntu: Distribution targetted at new users, with a focus on ease of use.
• RedHat: One of the most widely used distributions, mainly used on corporate servers. Does not have a direct free download, instead they support Fedora, but you can also get a free clone called CentOS.
• Debian: The most "free" / ethical distribution, see the debian social contract
• Suse: Very good hardware detection and input support
• Mandrake: User friendly desktop, used to be the best distribution for first time Linux users and desktops.
• Slackware: Lightweight, no complicated tools or configuration, simple installation, ideal for servers when you want to know exactly what is going on.
• Gentoo: Meta distribution where all the software is built from source using automated tools. Useful for making sure that the exact source code and build environment are controlled and readily available.
• YellowDog: for Power Mac
• TurboLinux: was once the leader in Asia
• Knoppix: Live Linux CD, with gigabytes of software ready to use without installation, great hardware detection