For those of you not familiar with the wide and wonderful world of Linux distributions; a trip over to DistroWatch.com can be a tad overwhelming. The typical Linux distribution (or distro from here on in) usually has a rather asinine name. Distros like Yellow Dog, Mint, Debian, Slackware, etc often have very odd origin stories behind those names that don't often give the slightest hint at what they have to offer to the user.
OK...Stop reading for a sec and hit up DistroWatch and read about the top 10 Linux distros here.
Ok now that you have read their reviews I am going to give you my unique perspective on a few. :D
Ubuntu / Mint
Or as I call it... "My Other Computer is a Mac" distros. Ubuntu and Mint Linux are hands down two of the best disros for new users. Their live cd's just plain work with no real need to configure anything beyond plugging in your wifi password (which is simple and intuitive). Also both distros have made adding new software to the system very easy via the GUI. I haven't played with Mint as much as Ubuntu, but it seems to share many of the same strengths. The only real "negative" aspect of Ubuntu is that it kind of locks the user into the GUI and the command line is given a backseat. Now you will need to trust me on this when I say at first this is great if you are new to Linux or have no interest in messing with the command line, but more experienced users will soon chafe under the lack of a proper root account.
Red Hat / Fedora / CentOS
These are the big names in enterprise level Linux. Big companies use these distros to get big things done. They are robust, they are tested extensively and they are deployed damn near everywhere. Lets look at Red Hat first. It has been around for a long time and since it started it has tried to make Linux more...profitable. Free open source software is great for the end user, but it requires a sound business strategy to make a profit from it. Red Hat does so by relying less on the open source community, and more on in house developers. They still publish a huge amount of code to the open source community in the form of Fedora their "free" (as in beer and lunch) OS. It is feature rich and is a great OS to learn as many of the programs included with it are also found in Red Hat Enterprise Linux. CentOS is a very popular distro that takes Red Hat Enterprise Linux and removes all of the non-open source software. The result is a very stable, very free, and very robust distro.
Please forgive my bias...SuSE and I go way back. Each time we have met... unfortunate things have happened lol. The first time I installed it was way back in 2000 and the YaST installer sucked...but to its credit, almost every distro of Linux was a bitch to install. But in my case, I totally nuked my new computer to boldly try Linux...and I was sorely mistaken in doing so. But even still...I gave it a second chance. Things haven't progressed all that well. They have their "build-your-own-os" site called SuSe Studio. In theory it is great, in practice it blows goats. Getting your personal distro to work is tedious and frustrating. Maybe I will take another stab at later...but not likely. SuSE is widely used in Europe as it was created in Germany. Also in many European nations they have to use open source if it is a viable option so it is widely used there. I can't recommend it. But again take that with a grain of salt.
One of the oldest and most respected distros around. The main thing that sets Debian apart though is its development cycle. IT IS LOOOOOOONG. Like years between releases. The reason for this is that Debian is like the universal OS. It can be slapped on anything from a clock radio to a server farm. The developers are kinda like the Marines...leave no architecture behind. They code it for all then release the update. Does this mean it is not secure or that it is a dinosaur before it is released? Hell no. They release security patches as they become necessary. Now, if you can't tell by the banner on my page I am a bit of a Debian fanboi. I don't view it as a real stand alone distro though...think of it more of a framework. When I install Debian I install it with just the bare essentials. Then I add on things bit by bit. Hell most times I don't even load a GUI (or a minimal x windows manager like fluxbox). For me this works and setup goes smooth every time. It should be noted that Ubuntu is based off of Debain...and Mint Linux is based off of Ubuntu. The main benefit of Debian is that can be used on a wide variety of hardware and it is a very stable build.