While there are too many Linux distributions for us to include them all, here are some of the most popular Linux distros, along with their download pages.
CentOS is a distribution based on source RPMs from Red Hat Enterprise Linux (RHEL), and strives to be 100% binary compatible with RHEL.
Damn Small Linux is a live CD distribution that fits on a business card CD and is light enough to run on a 486 computer with as little as 16MB of RAM.
Damn Small Linux mirrors, BitTorrent
The Debian distribution and Debian Project are governed by a social contract that requires that OSes produced by Debian will be 100% "free," as determined by the Debian Free Software Guidelines (DFSG).
Fedora, formerly known as Fedora Core, is a Linux distribution sponsored primarily by Red Hat, with significant community participation. The Fedora Linux distro produced by the Fedora Project was based on the original Red Hat Linux distribution and is made up entirely of free and open source software.
Fedora mirrors, BitTorrent
Note that the Fedora Project produces several "spins," including live CDs, DVDs containing the full set of Fedora packages, and boot ISOs for Internet installations of Fedora. See the installation guide to figure out which version of Fedora is right for you.
Freespire is the community-oriented version of Linspire.
Freespire download, BitTorrent
Gentoo is a source-based distribution, meaning all of its programs can be compiled from source code rather than installed as binary packages. That makes it highly configurable. Because the operating system and all of its applications can be compiled for the specific machine architecture it's installed on, Gentoo can perform extremely well. Gentoo is available for at least eight 32- and 64-bit hardware platforms. The distribution is more complicated to install than many others, but an active user community can help those who wish to tackle it.
Gentoo uses a package system called Portage that resembles FreeBSD's Ports. It lets you quickly install more than 10,000 pre-built applications.
Knoppix is one of the most popular live CD Linux distros.
Knoppix mirror network, BitTorrent, eMule
Linspire is an Ubuntu-based distribution whose chief distiguishing feature is the ease of installing new software with its Click-N-Run (CNR) installation utility. While Linspire costs $50, its sibling Freespire is free.
Linux Mint is an Ubuntu-based distribution that comes in two main CD versions. The Light Edition avoids non-free patented software. The Full Edition includes proprietary plugins and codecs. Both use the GNOME desktop environment by default. You can also download a KDE Community Edition DVD or miniKDE Community Edition CD, or an XFCE Community Edition CD.
Mandriva Linux, formerly known as MandrakeLinux, is an RPM-based distro that was originally designed to be binary compatible with Red Hat Linux. Mandriva produces versions of its Linux distribution for consumer desktops, corporate servers, and for high performance clusters. Some, but not all, versions of Mandriva are free to download.
The openSUSE project is sponsored by Novell to create a base for the SUSE Linux distribution it sells and supports. The openSUSE distribution is worked on by Novell employees and community members, and is suitable for desktop and server use.
You can find openSUSE downloads at download.opensuse.org, but it may be a little confusing. The project offers multiple ISOs for CD installation, DVD installation, and network installation. You can also find BitTorrents for the various downloads, and a live DVD. If you're not quite sure what you need, visit the download guide, which explains the release table, and what development versions may be available and how stable they're likely to be.
PCLinuxOS is a popular Linux distribution distributed as a live CD that can be installed to your hard drive. Originally based on Mandriva, PCLinuxOS is now a solid distro in its own right that uses APT and Synaptic to manage packages, and some of the original Mandriva administration tools.
PCLinuxOS download mirrors, BitTorrent
Puppy Linux was written from scratch with two goals in mind: speed and ease of use. At boot time the entire system loads into RAM and runs from there, which significantly boosts the system's overall speed, and lets you run Puppy on a diskless workstation or thin client. It downloads in only 90MB, and can run as a live CD. It also comes with a remastering script for creating derivative distros, which other developers have used to build Puppy-based distros (called puplets), including NOP, GrafPup, and EduPup.
Sabayon Linux is based on Gentoo and supports both i386 and AMD64/EMT64 architectures. It comes in a 4.7GB live DVD release, a Professional version based on the stable branch of Portage, and a 700MB CD Mini version. While Sabayon contains proprietary drivers, free software fans can disable them at boot time.
Slackware Linux is the world's oldest surviving Linux distribution.
Slackware download page, BitTorrent trackers
Ubuntu is a popular community-developed Linux distribution for laptops and desktop machines, and is also gaining popularity on servers. Ubuntu is based on Debian GNU/Linux, and also serves as the foundation for several other Linux distributions in its own right.
Ubuntu download form, Kubuntu, Xubuntu, and Edubuntu.