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.
   Additional loggers could also be run on-device, such as a wifi connectivity checker or a Fing server.
   If you have a smart home setup, you could also log state data or energy monitoring history at a particular interval, or run a homebridge or homeassistant instance.

Edit: list subitem formatting messed up

Home Assistant for family members

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.

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.

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.

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

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.

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.

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.