This is a topic which will surely create some controversy. Everyone have different views regarding the various distros of the linux. Even the topic is highly subjective, I have tried to put various distros of the linux in different category for the best distro of that category.
Most Popular
Why does it matter which distros are most popular? They generally offer more resources: larger free software repositories, more tutorials, better doc, more support, and active forums.
Well, the title of most popular is taken by Ubuntu which also include Kubuntu, Xubuntu, Lubuntu, Gubuntu and others. Canonical claims 22 millions ubuntu users and 1.3 million servers running Ubuntu and 22000 new users joining each month.
The next spot in this category will surely be Red Hat.The Red Hat family includes Red Hat Enterprise Linux, CentOS, Fedora, Oracle Linux, and others. I've seen estimates that Red Hat has over 12 million users and Fedora over 1 million. Red Hat is the first billion dollar Linux company
Most User Friendly
The first spot according to me, should go to Mint. Well, Mint is based on Ubuntu, but still is provides far more different user environment than regular ubuntu. Since it is based on Ubuntu, it also enjoys the perks of Ubuntu that include huge software repositories, a familiar system, a big user community, etc. Mint protected their user by providing with the mate and cinnamon. The former is contribution of GNOME 2 interface and latter have GNOME 3 interface.
Many other distros can also cite the spot of most user friendly, but Mint philosophy of capitalizing on Ubuntu while addressing its shortcomings is a winner.
Best Live Distro
The live OS is that which can run right from any bootable flash drive and include all features of a OS to maintain and work on the system.
The first place in this category should be taken by Puppy Linux. This distro can run on any computer right from the flash drive without even the need for installing it. It can run systems that even have some component broken or very laggy computers or systems with lot of restrictions.
It is the distro with just 130 MB of download size, it can run entirely from the memory of the system, at least 256 MB.
Best for older Computers
If you have an older PC, like a Pentium IV or III, (or even a II!) you need a distro that will run on minimal hardware. It should also be tested on older machines. Puppy Linux fits the bill. It can make your old Windows XP or 98 computer useful again.
Many distros theoretically run on older hardware but they don't have a large user community running mature systems. Join the Puppy forum and you'll see that you're in the right place.
Best Office Desktop
The office desktop requires the most out of the system which includes office software, email client, calendering and contacts manager. With such requirements everyone have only distro name for it , that is OpenSUSE.
Not only does OpenSUSE come with all the bundled apps you need in the office, it also supplies consistent, user-friendly interfaces. No jumping off the deep end with OpenSUSE: you're not forced into the Windows 8 UI or Unity. So you can just get your work done.
With applications like LibreOffice and Wine, you can co-exist with organizations still using Windows and Office. LibreOffice allows you to interchange office files while Wine runs over 20,000 Windows apps under Linux. (LibreOffice and Wine run on nearly all Linux distros.)
Best Support
If you are looking for the paid support for the linux system that Red Hat is the best way to go. It have great service to offer to maintain your system and a nice user interface. But unlike other distros , it a paid version. Oracle Linux works really well with server database and various offering from the oracle.
For Hackers
If you are into hacking and hopes to continue the legacy with the linux, then Back Track is the best available option for you. Back Track provides with the various vulrability testing software right from the installation. It comes with various application which help to find the vulrability in the system and provides with many other software which helps to do so.
So, these were the various distros of the linux by category. I really hopes this will help you to choose the best linux distro. I would like state it again that, all distros of the linux are good in their own way, but what makes it best is what you are looking for in it.