the most popular distributions that i know of are these:

1. RedHat Fedora Core Distribution - Fedora would have to be the most popular beacause its very easy to use and very easy to install

2. Ubuntu - Like fedora, this distribution is very easy to use and has very good support

3. SuSe - i never installed Suse before, so i dont know

4. Caldera

5. Debian

there are other but these are the ones i can think at the top of my head. :)

 

Distribution Features Platforms Web Site
Fedora Project the inheritor of the previous red hat distributions, the entirely open source fedora features tools and useful in any linux environment. includes GNOME, KDE and RPM desktops I386 redhat.com
Red Hat Enterprise This package and several variants represent the latest iteration of what had before of the standard linux distributions a carefully managed upgrade program intends to bring greater stability and integration to business users. this system is not available for free. its not open source x86, itanium, Alpha, SPARC, Mainframe, M68k redhat.com
SuSe Linux this distro is from germany and its freely available and offers software packages for many business needs. comes with GNOME KDE and RPM x86, itanium, Alpha, SPARC,PPC suse.com
Slackware Linux this distro come with GNOME and KDE. prides itself on being "UNIX-LIKE." x86, ALPHA, SPARC slackware.com
Debian Linux debian offers the largest number of packages of all distros. it contains software packages for any use and ships with GNOE KDE, the debian package manager and RPM x86, ALPHA, SPACK PPC debian.org
Turbo Linux this is the most common distro used in asia. it is famous for its clustering abilities. it comes with GNOME KDE and RPM x86 itanium ALPHA mainframe turbolinux.com
Mandrake Linux this is a user oriented distribution similar to red hat with enhancements for ease of use. it comes with GNOME KDE and RPM x86, PPC linux-mandrake.com