This is an incomplete list of the distributions I have used in the past with a small review and link to the home site. I will be adding to this periodically.
ORDERED BY RELATION
Debian and Debian Forks
Debian - Stable and easy to work with. A common conflict with Debian is the age of the packages but you can still build from source, just more time consuming. Though not approved as Libre, it does have a Libre option and a ISO with firmware support. Highly recommended for advanced users.
Ubuntu - Coming in a variety of flavors in regards to the window manager makes is approachable in every sense to ease of use. Newer packages available and supporting most if not all common utility and software available. This distribution would be best for those who do not care about the Libre focus and want to have a one size fits all distribution. Recommended for beginners.
Mint - An Ubuntu fork without the bureaucratic issues that Ubuntu brings to the table. Cleaner in theme and simplicity. I would recommend this over Ubuntu if Debian is not your speed. The Mint team does have a spin base on Debian though I would stick with their default due to the simplicity it provides. Recommended for beginners.
Elementary - Another Ubuntu fork with Pantheon as a window manager. Though these features does not make it a more interesting option over Mint. If you are a fan of Apple type re-skins or the OSX feel, this is your distribution. Recommended for beginners.
MX - MX is an interesting blend of the discontinued Mepis project and AntiX, designed to be a portable, clean, full desktop to be booted from USB, this is a preferred distribution if you need to take your work on the go and are concerned about security or project integrity. I have used this distribution for about a year with no issues. Recommended for advanced users.
AntiX - The sister project of MX, this is a much smaller more RAM friendly MX Linux. The function and fashion of MX in a smaller package. DolphinOracle is heavily invested with this project as well as MX Linux. I would recommended taking a look if you are a minimalist users in need of a portable system. Recommended for advanced users.
Devuan - A full Libre and Systemd free Debian, enjoyable experience. Though does have a slower release cycle than Debian due to the package restrictions. If systemd is a concern for you as a user, this may be a good stable experience you are looking for.
Trisquel - A full Libre Ubuntu, very comfy and clean. I would recommend this to anyone wanting to use a Libre distribution while maintaining an easy to use environment. Trisquel comes in both a Mini-ISO and a Full-ISO based on your own personal preference.
Tails - A Debian fork that boots from USB and traffics all data through Tor. Perfect as a portable system for browsing the web and maintaining a clean work space. I would recommend to any user who needs a secure system to work from.
Heads - A full Libre alternative to Tails.
Kali - Forked from Debian and the successor of Backtrack, this is the industry standard for a boot from USB penetration testing distribution. If you are looking to learn about secure systems and Pen-testing, Kali is for you.
Parrot - Another Debian fork pen-testing distribution, I would recommend this distribution as a space to live in and use as a daily driver, packaged like Kali, with more ease of use packages.
Red-Hat/Fedora and Red-Hat/Fedora Forks
Red-Hat - Red-Hat Enterprise Linux or RHEL is a Linux distribution developed by Red-Hat designed for the commercial market. Red-Hat uses strict trademark rules to restrict free re-distribution of its officially supported versions of Red Hat Enterprise Linux, but still freely provides its source code. Third-party derivatives can be built and redistributed by stripping away non-free components. While I do not recommend using Red-Hat, instead I would recommend the RHEL fork CentOS, it is certainly an interesting project.
Fedora - A Red-Hat owned project and is considered the bleeding edge version of Red Hat. Fedora closely resembles Ubuntu in its alternate versions and flavors called Spins. I would recommend if you are new to Linux or want a more Business Like Experience than what Debian and Ubuntu can give. This can also be a recommended alternative to hobbyist users wanting to use Kali Linux or another specialized spin.
CentOS - CentOS is a compatible rebuild of the Red Hat Enterprise Linux, in full compliance with Red-Hat distributions. CentOS is for people who need an enterprise class operating system stability without the cost of certification and support. For those who are needing a solid server base or want to have something as stable as Debian, this is highly recommended.
Qubes - Based on Fedora and similar in function as Tails, it uses the concept of compartmentalization and virtual machines to maintain a secure work-space. Though it takes modern hardware to run smoothly. Highly recommended for security focused users.
Arch and Arch Forks
Arch - This is a branch of Linux for those who demand a higher need of control over their system in terms of software. Arch having the availability of bleeding edge software and the Arch User Repository makes have a system that meets your needs possible. Though installation involves more knowledge or at the very least, the ability to follow instructions. I have never found arch to meet my needs due to my compulsive need to purge my system often. Recommended for Advanced and Expert users.
Antegros - Now discontinued, this was a prepackaged Arch with an installer for newer users to play in an arch like system.
Parabola - A full Libre variant of Arch and systemd free. For those looking for a more Libre experience I would recommend taking a look here.
Hyperbola - A full Libre variant of Arch with Debian security parches, also is systemd free.
BlackArch - An Arch system that has more tools packaged that you should or would ever need. The ISO is about 10gb. If Kali and Parrot are Swiss Army Knives, BlackArch is a Swiss Army Toolbox, Clunky and Heavy but you will have a tool for that.
Gentoo and Gentoo Forks
Gentoo - A must try for a more experienced Linux user. This is the distribution to try if you demand full control over a system, using Python ports for all packages and building from source, it meets the Debian stability with Arch bleeding edge. I would recommend for any user wanting to learn more about Linux.
Calculate - A more user friendly Gentoo. Has an installer and pre-installed packages for the average user. Great if you want to experiment in the Gentoo system.
Funtoo - Gentoo with more Dev features and a rolling 12h release cycle.
Pentoo - A Pentesting packaged Gentoo, I would not recommend this unless you are playing CTF in a convention tournament. Packaged like Blackarch and built from source. But buggy and difficult to maintain.
Puppy Linux - Similar to AntiX with the boot from USB functionality and similar in size. Though the packaging and functionality is lacking. I would recommend AntiX over Puppy.
Fat-Dog Linux - Also similar to Puppy and AntiX but now forked from Linux From Scratch, due to the build Fat-Dog brings it makes itself a easier and more utility friendly sibling of Puppy.
Void - An independent distribution, Void features a hybrid binary/source package management system which allows users to quickly install, update and remove software, or to build software directly from sources with the help of the XBPS source packages collection. Rolling-release development model with daily updates and init system called "runit". Recommended for those wanting something unique while being systemd free.
FreeBSD - FreeBSD use is far reaching and well documented in computing history. Use range from server software, databases and web servers, to desktop software, games, web browsers and business software - all free and easy to install. FreeBSD is highly minimalist and I would recommend for those looking to install a Unix system. However advanced users will be more at home here.
TrueOS - A easy to use and install FreeBSD fork, for those wanting to learn and use BSD.
OpenBSD - A security focused BSD, installation is more difficult than TrueOS so reading is needed. Though security is top notch compared to other Linux and BSD distributions.
HardenedBSD - A security focused FreeBSD fork. HardenedBSD prioritizes exploit mitigation and cryptography.