RedHat is probably the most recognized and specified distro in the business community (ie by managers as opposed to IT people. A lot of the documentation at http://tldp.org was based on (Pre-Enterprize) RedHat, and the book Running Linux, and excellent introductory reference, was based on it. Running CentOS, the recompiled open version, or Fedora, the "community" based free version is a good way to learn the Red Hat Way.
Debian, on the other hand, is probably the most used Server OS, excluding the above enterprize environment. When the IT staff have chosen the distro instead of Marketing or Management, the server run Debian. It's upgradability, reliability, and long-term stability are second to none.
A lot of the popular distributions are re-workings of Debian that use newer packages. Ubuntu, Mint, and Arch are all based on Debian, as are many others. Mandriva is the main Red Hat based distribution that's not affiliated with Red Hat. SuSE uses the same package system as Red Hat, but is very different. Gentoo and Slackware represent their own branches of the tree, with Slackware being one of the oldest.
Ubuntu is the populist. SuSE is the Novell of Linux, IBM bases it's POS systems on it. Gentoo was the most popular a few years ago, but is a hobby unto itself.