• Debain: Debian is my current distro of choice. It is very easy to maintain and upgrade, has very powerful system administration tools, and is designed from a more cautious standpoint than most other distros. However, it can be a beast to install and setup the first time, making it not the best distro for newbies.
• Progeny: Progeny is a Debian-based commercial distro. It's actually made by some of the original Debian people. It is much easier to install than vanilla Debian, and you can upgrade it with all of Debian's packages. So I would recommend it for anyone who wants to use Debian, but doesn't have the skill to install Debian. However, on it's own (forgetting the Debian packages you can use with it), Progeny is a pretty weak distro. 2001-10-30: Apparently Progeny will not be making any more releases... so it looks like it's no more. This is too bad because I personally felt this distro was doing things "The Right Way (tm)".
• Red Hat: Red Hat was my first exposure to Linux. I used it up to (and including) Red Hat 6.2. Red Hat is an RPM-based distro (indeed, they were the first, since RPM stands for "RedHat Package Management" ;-) Red Hat was the first distro to really be easy to setup. Currently, Red Hat is a half-way decent newbie distro, IMHO, but has default settings geared too much towards server applications to be much of a desktop OS. Red Hat has had some problems with many of their packages recently (both security problems, and compatability problems), combine this with the fact that RPM-based distros are not as easy to upgrade as Debian-based distros and you can see why I made the switch ;-)
• Mandrake: Mandrake was originally a repackaging of Red Hat (it started as Red Hat distros, with more security updates, and some new packages), but has since evolved into a wholly unique Linux distro. Mandrake's main focus is ease of use and setup. IMHO, it is the ideal distro for newbies and (some) desktop users. It is, however, an RPM-based distro, which means it can have problems with upgrades (granted, it's still far easier to upgrade than a Windows machine... but I digress ;-)
• Peanut Linux: Peanut Linux is what I like to call a "Psuedo-Embedded" distro. It is very small (approx. 85Meg download, last I checked), runs very lean, and yet contains a wide variety of desktop applications. This makes it a perfect desktop or gaming OS. It's not proven to be easy to upgrade (as a matter of fact, there have been some major compatability breaking changes in it the last few versions), but it is simple enough to install and setup that for very limitted uses (desktop OS, laptop OS, gaming OS) you can forgive this.
• PLD: Polish Linux Distribution is an attempt to make an RPM-based dirsto "The Right Way". They have learned from previous RPM-based distros, and from Debian-based distros, and have decided to combine the best of both worlds. PLD aims at being as easy to maintain as a Debian-based distro, but with the ease of packaging (for developers) of an RPM distro. How are they doing this? They are using something very similar to apt-get, but for RPMs. This distro is still early in development, and not very complete, but it shows a lot of promise.
• Vector Linux: This is another "Psuedo-Embedded" distro similar to Peanut (as a matter of fact, I think Peanut may have been originally based on this). It is another very lean and light distro perfect for desktops and gaming. Evil3D.net loves this distro.
• SuSE: This is another RPM-based distro. I honestly haven't had much experience with it, but from what I hear it's a pretty good distro. I do know that they were one of the first distros to offer ReiserFS support, and that they fund a lot of very important projects (well, important to me, like the next generation Linux input/joystick drivers).
• Slackware: This is one of the classic distros (Debian and Red Hat being the other two major classics). I haven't had much experience with this distro lately (though, I did work with it at a job I had back in 97), so I can't say much about it. But I do know there are a lot of people who swear by it. I would guess it's not a simple distro to install (that it would probably be on the level of Debian). Slackware uses it's own package format (not RPM and not DEB), which I know little about (except I suspect it's just tarballed packages containing file trees branching out from the root directory, but I haven't verified this).
• Gentoo: Gentoo is part of a new breed of Linux distros. Instead of supplying pre-compiled, binary packages, which are built generally so that they can run generic systems (such as EVERY other distro listed here), these new distros provide packages of source code, and automatically compile them on your hardware. What's the advantage? It can make your OS and its applications run much faster (since they will be optimized for your hardware). It can also elliminate some of the problems/flakiness that generic builds bring. What's the disadvantage? Installation and upgrade will be extremely slow, since every package will be recompiled. Speaking as someone who just recentlty rebuilt his Laptop's XFree86 from source, large package rebuilds are very slow (XFree86 4.2 took nearly three hours to build on my 500Mhz Celeron laptop!) Still, I think these new "Source-Based" distributions are really something to watch!

For more distro info, please check out DistroWatch.com.