Friendly - some are friendlier than others. Mint looks particularly interesting.
Ubuntu, currently the 500lb gorilla of the free linux world. Very mature, easy to install for newbies. The upside is you can believe the hype; it's ready for primetime. The downside is that it can be bloaty (by linux standards, at least).
Recommended for most general purpose uses and those with faster, newer machines
Kubuntu, Ubuntu with the KDE desktop environment instead of Gnome
Lubuntu, Ubuntu with the very lightweight lxde desktop environment. Use this Ubuntu flavor if your machine is not as recent or you prefer speed to bling.
Recommended for those that prefer speed.
Xubuntu, Ubuntu with the somewhat lightweight Xfce desktop environment.
Recommended for those who think gnome and kde are bloated.
Edubuntu, Ubuntu packed for teachers, requiring minimal setup time and an easy interface for students.
Recommended for teachers and students.
Ubuntu Netbook Remix, a version intended for small-screen netbooks and laptops. Distinctive desktop appearance maximizes usable space.
Debian. Intensely conservative and methodically plodding, this distro is extremely stable and has bulletproof free software cred. There will be no non-free software on your Debian box unless you put it there. Famous for the most robust package manager (.deb). It is the source of many derivative distros such as Ubuntu, DSL, Knoppix, Xandros, Linspire, etc.
Red Hat / Fedora
Famous for the first successful, widespread use of a package manager (.rpm, in this case).
Slackware, the oldest existing distro. Very plain and conservative; makes Debian look like a drug fiend. Recommended for folks that prefer "the vi way of life".
Small / efficient
Damn Small Linux (50MB), pioneered the "smaller is better" idea in linux, and stays small enough to stay on one of those 50MB business card CDs. Downside: ugly/cartooney desktop, 2.4 kernel.
Damn Small Linux - Not (100MB), a DSL fork with a prettier desktop, and modern 2.6 kernel.
Tiny Core Linux (10MB !), a very lean distro with zero installed apps. You have to install everything you want. Not for the timid or the inexperienced.
SliTaz (30MB). Similar to DSL in intent, but somewhat smaller with a modern kernel. Not for beginners.
FreeBSD, the Betamax in the Betamax/VHS wars.
For whatever reason, BSD variants got left behind in the free *nix race. Here's a good page for newbies to start.
the mousepad
antiX, based on Mepis (Debian). Installs with fluxbox/IceWM rather than a heavier DE. Fantastic livecd functionality.