The first one that came to mind was fli4l (Floppy ISDN for Linux). Originally a distro of German origin that fit on a single floppy disk to turn a 386 or 486 PC into a router for ISDN connections. Last I looked it's still actively worked on.
There are probably tons of more obsuce ones. But this is one I actually used.
Smoothwall. I used to run it a lot back in the early 2000s for personal use and even helped set up a couple small businesses with it but I don't hear of anyone else using it these days, people seem to love openwrt and pfsense more.
It was great for just taking any old x86 machine and making a powerful, fully featured firewall/router out of it, including a VPN server, all through a web interface. Nowadays that's boring shit but in 2002 it was pretty cool.
they have a wiki with insane nonsens about why they don't package certain things. Example:
pam
Package has different security-issues and is not oriented on the way of technical emancipation as Hyperbola is trying to adapt lightweight implementations.
you think a distribution that automatically includes all the proprietary stuff that we use baked into the distro would be more popular since it makes linux ready to go for most people; but it still gets fewer than 300 clicks per month.
it's main feature is that it completely redefines the system's root directory structure. the only reason i even know it exists is because i'm friends with one of the creators
Limiting to those I have used daily and treated as Linux (used the terminal for example) probably Maemo. I used to carry my Nokia Internet Tablet 770, and then my N800 everywhere with me.
Maemo is also an ancestor of both Tizen and Sailfish OS
Well I don’t hear much about Gentoo, Damn Small, Puppy or Knoppix anymore. Wonder if they still exist.
I haven’t done much disto hopping since I settled on Ubuntu around ‘08 and then on NixOS last year. I like my systems working when I need them and waiting around for a new install to finish is boring to me.
I imagine there was a time when this wasn't obscure, but I'm guessing people today don't remember Caldera OpenLinux. That was the first Linux distro I installed/used. A guy from church gave his copy.
Caldera eventually became SCO. But I'm pretty sure I was using Caldera OpenLinux before the whole Novell patent suit thing.
Sabayon Linux. I'm not sure if it's still releasing updates, the main website is dead. It was based on Gentoo and later funtoo, but had a package manager of precompiled binaries. You could still use emerge if you wanted to. Definitely a weird and interesting distro
Blend OS is trying to do the declarative nixos thing but with an arch base. That's pretty cool.
ClearOS was Intel's attempt at an immutable os. From what I remember it was really fast.
Edit: actually it clear Linux not clearOS.
Edit: also clear Linux is stateless. I don't know, there's a lot about it I don't understand
I haven't tried all that many distros, but I'd say Puppy Linux. Pretty neat that it loads into RAM from USB and has fairly light memory requirements, but it does feel a little on the clunky side as far as configuration and stuff goes.
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
Jolicloud. I ran it on an old low-spec netbook in 2013ish, basically a ChromeOS before Chromebooks were a thing. It was discontinued in 2016 but great for the hardware while it lasted.
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.
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.
I used to run Reborn OS at around 2017 for a few years. It used Cnchi installer, just like Antergos, and when Antergos died, I saw Reborn as its successor. But the title went to Endeavour (why?) and Reborn never got popularity.
Not super obscure, but not many talk about it. Q4OS, I love it, a perfect windows replacement down to even imitating the old style windows installer. Plus it's Debian based so it has a lot of support. I plan on moving my grandparents to it when windows 10 gets fully discontinued as their current rig doesn't support 11
Longene Linux. Linux-based operating system kernel intended to be binary compatible with application software and device drivers made for Microsoft Windows and Linux.