These distros listed here include only 100% free/libre software, and those that can be used with only free/libre software. They are listed in alphabetical order.
Debian is fully free software out of the box, however they maintain a repository of proprietary software - you can always choose not to use those.
An independent GNU/Linux distribution based on concepts of simplicity.
Fedora is also fully free software out of the box, however there are still proprietary blobs in their kernel. It's possible to switch it out with the Linux-libre kernel.
You can always choose to build Gentoo with only fully free software included and with the Linux-libre kernel.
An advanced GNU/Linux distro built on top of GNU Guix (pronounced “geeks”), a purely functional package manager for the GNU system.
A long-term support simplicity-focused distribution based on Arch GNU/Linux.
Like Gentoo, you can always choose to build LFS with only fully free software included and with the Linux-libre kernel.
A distribution based on Arch that prioritizes simple package and system management.
A GNU distribution based on Debian with a focus on privacy, security, and convenience.
A GNU/Linux distribution based on Ubuntu that's oriented toward small enterprises, domestic users and educational centers.