Selfhosted

1. DNS resolver, like pi-hole, unbound with adguard, diversion, etc.
2. RMS server: a lot of Remote Desktop software has the option to install a listener on a low power device elsewhere on the network that can use wake-on-lan to access computers within the network without keeping everything on 24-7.
3. Log aggregator: would be useful for anyone who troubleshoots stuff regularly, but historical info of any kind can come in handy.
   Simplest form might be a scribe server. Network gear often has an option to send logs to a particular URL, so if you added the scribe server IP/port to the field you’d have historical network logs.
4. Additional loggers: could also be run on-device, such as a wifi connectivity checker, smart home or energy monitoring state data, decibel meter with USB microphone
5. RADIUS server for managing enterprise WPA keys
6. Mobile home: due to the size and power draw, when paired with a hotspot and battery the potato could be useful as a mobile service repeater, a VPN client that deploys your home services on the go (e.g. in a vehicle, hotel room, family/friends’ houses, etc) to arbitrary client devices. If you use the same SSID/PW and encryption type, personal devices would use it automatically during travel.
7. Home theater box like kodi or jellyfin client

At the level of individual apps, the list explodes. Many progressive web apps can be hosted essentially for free on the potato, so you could shunt your always-on services to this machine to allow low power states on a beefier machine. For example:

1. Network management or security software like Fing
2. Low throughput NAS or incremental backup management server like rdiff, TimeMachine, etc
3. inventory management like partkeeper, storaji, etc
4. Smart home bridges like homeassistant or homebridge
5. Bookmark aggregator or landing page like heimdall, raindrop, pinalist, etc
6. Retro game emulators or ROM libraries like retropie
7. Photo libraries like photoprism
8. Book libraries like calibre-web

Edit: list subitem formatting messed up
Edit: add common micro services, mobile deployment
Edit: add home theater suggestion
Edit: add always-on and PWA examples

I run Pi-hole and PiVPN on my Pi 0W.

Sensors. Especially sensors in your living space where fans or other noise from the proper server would be distracting, or in a tight space - inside your HVAC, for example - where a proper server wouldn't fit.

Media front-end. Most of those SBCs are more than enough to run a kodi or jellyfin frontend, fanless for minimum distraction.

Robot. Low power requirement so it could be mobile; but there are lots of stationary possibilities. GPIO libraries are great for running servos and there's tons of libraries to facilitate.

Home Assistant for family members

Media server client, pihole, emulation, programming or home automation project. You could even prop it up as a standalone web server and make some kinda creative thing.

Lower power draw is about it. But there are now x86 SBCs that can also run on as little as 6W so there's no reason to compromise and use ARM's non-standard fragmented BS.

Donate it.

Using it just draws more power.

Single board computers have GPIO and interfaces like SPI and I2C. They also tend to have lower power consumption and can run from 5 volts. If you want to interface with low level hardware or run from batteries, the SBC will usually be the better choice.

As mentioned many times I'm sure, I use my rpi's as a pi-hole/VPN. It's nice having them as dedicated devices for low power things, if my main server ever fudges up, my VPN still works and internal DNS is still resolved. If I'm not home and get complaints from the family that jellyfin isn't working, I can either fix it remotely or wake up my dev server for them to use in the meantime.

I also have an rpi 1 as a "dedicated ssh machine" that I can ssh into in case all of my other machines have gone goofy. If for any reason my two main devices aren't accessible, that one will be because if there's power to the house it will turn on. It does literally nothing else, so there's very little chance a power outage will corrupt anything. It does require that the pivpn device is working if I'm not home, but I prefer to leave that to it's own ...devices.

I have an Rpi4 4gb model and run Uptime-Kuma who's sole purpose is to monitor my server and alert me if it should go down. I also have it acting as a Tailscale exit node.

If you're interested in home automation, I think that there's a reasonable argument for running it on separate hardware. Not much by way of hardware requirements, but you don't want to take it down, especially if it's doing things like lighting control.

Same sort of idea for some data-logging systems, like weather stations or ADS-B receivers.

Other than that, though, I'd probably avoid running an extra system just because I have hardware. More power usage, heat, and maintenance.

EDIT: Maybe hook it up to a power management device, if you don't have that set up, so that you can power-cycle your other hardware remotely.

Run Vodafone's Dreamlab on it and donate CPU cycles to research.