Like everyone else, I have my favourite GNU/Linux distribution, so I am wearing my asbestos suit. Please note that I am only discussing the versions for PCs.

Linux is Linux. Distributions differ because of
what they leave out,
the packaging system used,
the installation system,
and the processor (i386, i586, amd64) they have been compiled for.

How is the Linux system going to be used?

The first question you need to ask yourself is, "what am I going to doing with Linux?"
The second question is, "what am I likely to be doing with Linux in 3 - 5 years time?"

You can do anything with any distribution by adding/deleting packages and by modifying configuration files. So this has to be treated as a general guide. Wanted applications can be downloaded or purchased

(1) Those who want to see what GNU/Linux is like with risk or hassle.
Suggestion - Knoppix, Ubuntu Live.
A fully featured live CD. This works from a ramdisk in memory and the CD. It does not touch the Hard Disk(s) and so will not affect the existing operating system. It boots from the CD and is the equivalent of a 2000 MB installation. This not a true installation, but it can be installed onto the HD.

(2) A novice to Linux/unix who wants to get a system running as easily as possible and who is unlikely to be doing any kind of serious technical work in the future.
Suggestions - Ubuntu, Mandriva, Fedora, CentOS.
Red Hat(tm) was the most heavily promoted and popular free distribution so friends and colleagues were likely to be using it. Time will tell if Red Hat Fedora will achieve the same status.

(3) A novice who wants to get a system running quickly, but who expects to get involved in the more technical side of GNU/Linux in the future.
Suggestion - Ubuntu, CentOS.
These are easy to install and setup, so the system gets running quickly. See scenario (5) below.

(4) A home office or small business user who is prepared to buy applications and support.
Suggestion - Mandriva, SuSE, Red Hat commercial versions.
These distributions are aligned to the commercial user.

(5) System administrators, developers and people who want to get into the nuts and bolts of Linux/unix systems - including those who want to learn fast.
Suggestions - Debian, Slackware, Smeserver (for servers)
Debian is maintained by a team of high powered volunteers who have an interest in technical side of the distribution. The operator has full control of the installation and this makes it rather tedious to some newbies. It is also "politically correct" by sticking strictly to the concept of free software.
Slackware is the oldest surviving distribution and comes from the days when "men were men and Linux was Linux". It has a loyal following.

(6) Computer retailers who wish to sell machines with a pre-installed Linux system.
Suggestion - Ubuntu. The simplest and fastest installation about. A very stable distribution.

(7) Someone who wants full support.
Suggestions Ubuntu, Red Hat, SuSE.