Linux

I see no one has mentioned Bedrock Linux yet. Not sure though how others would rate its 'obscurity' though. It's definitely a standout among distros.

There was a bunch of weird rebadged Ubuntu derivatives back in the day.

Ubuntu satanic edition. https://archiveos.org/ubuntu-satanic/

Ubuntu Christian edition. https://archiveos.org/ubuntu-christian/

Hannah Montana Linux https://hannahmontana.sourceforge.net/

Probably KaOS. It puts a strong focus on KDE and Qt.
As in, it doesn't package programs using different GUI toolkits, aside from the most popular, like Firefox and GIMP. When I tried it a few years ago, you also had to enable a separate repo to get access to these.

No one mentioned Bunsenlabs or Crunchbang Linux here, but they aren't really that obscure.

If being usable is a metric, Slackware

There was this distro that stuffs everything of a package in one folder, instead of /usr/lib & co. What was it called again?

2 days ago my friend found an old SATA hard drive and gave it to me to check what's on it, and me, not having a disk station or anything, and against all better judgment, I just swapped the disk in my laptop for my friend's, and instead of my laptop being fried it turned out the disk was running something called Crunchbang Linux

dyne:bolic - specifically 1.4.1

Had support for the original Xbox, a multimedia editing / streaming focussed OS. I'd never run it on mine - just messed with xdsl before going back to XBMC.

Maybe not some obscure ones, but here are some lesser known ones:

Talos Linux. It's an immutable operating system designed specifically to deploy kubernetes.

OpenSuse Harvester Think Proxmox, but instead of VM's and LXC containers, it's VM's and Kubernetes.

XCP-NG is a RHEL based distro designed for managing Linux virtual machines using the xen hypervisor, as opposed to KVM. Think Proxmox, but RHEL and Xen (also no LXC). However, it does not come with a web ui out of the box, you have to deploy it yourself. Technically, XCP is a Xen distribution, since Xen is a kernel with nothing but a hypervisor that runs under the main distro, but the primary management virtual machine is RHEL based, and uses Linux.

Speaking of Proxmox, Proxmox is technically a Linux distro.

SnowflakeOS is a project that aims to bring a GUI focused experience to NixOS.

TurnkeyLinux (site is loading very, very slowly for me right now) is not a single distribution, but rather a set of debian based distributions that are designed to be turnkey appliance virtual machines that contain and host a specific app. To deploy the app, all you have to do is set up the virtual machine.

Now, here are some not-linux, but interesting distros:

SmartOS. They ported KVM to unix, and also can use Linux syscall translation (similar to wine) to run apps in containers as well. There is also Bhyve. It's a very interesting hypervisor platform.

OmniOS is similar. Bhyve, KVM, and Linux syscall translation in containers.

Not really a Linux distro, but TempleOS

Clear Linux.

Sabayon Linux

I used it for a few years, great distro. I think it's dead now. It was based on Gentoo but with thoughtful defaults and a very good binary package manager.

also Funtoo Linux, but i never really used it

No one ever mentions Crux Linux

SLiTaz

It's an obscure originally live usage oriented distro that you could also install. It was the first *Nix I ever used.

I created a distro once for class that just had diaspora installed on a live CD. It was only used for demos a looong time ago. DiasporaTest.

I had no idea mageia existed until I met a dude who had it