This is a wide discussed topic, and everyone has his own opinion. I'll show mine here for your reference only.
I have used several distributions of Linux: RedHat, Debian, RedHat Enterprise Linux, CentOS, Ubuntu, Slackware. And I also have tried several others: Arch Linux, Gentoo, openSUSE. The only one UNIX I have used is Solaris 9. I've tried FreeBSD, but failed on my box. 😦 What's more, I have read a little of Linux From Scratch book.
How to select which distribution to use? The best is the one which satisfies your requirement.
My first consideration is package management. RPM & DEB are two of the most popular ones. I personally like DEB more. RPM has been criticized in the old time, especially because of its dependencies hell. (YUM is a good tool to solve it now.) DEB always put dependency on its first consideration.
Popular distributions using RPM: RedHat Enterprise Linux (RHEL), Fedora, CentOS, openSUSE, Mandriva, etc. Popular distributions using DEB: Debian, Ubuntu, etc.
For RPM distribution servers:
If you can pay for it, I think RHEL is the best in RPM distributions. If not, CentOS is enough.
For RPM distribution desktops:
Fedora, openSUSE, Mandriva etc. all work well.
For DEB distribution servers:
Between Debian (stable) and Ubuntu LTS, I prefer Debian.
For DEB distribution desktops:
Ubuntu is a good choice.
If you have enough time and like to use blooding-edge software, try Arch Linux. If you like to use old, stable software, but optimized for your own box, use Gentoo but DON'T compile too often —- it's a waste of time. If dependency problem is not your main consideration, and you are going to customize your own distribution, Slackware is a very good start. If you are zealot of open source and like to compile everything yourself, enjoy Linux From Scratch (LFS) please.
I use Slackware for desktop, and Debian stable for server (no X).