I use one of my PIs as a backup for my OpenBazaar store. I have it set up to do an rsync on my store's VPS. If I ever need to switch it for some reason, I can just run a few commands to enable the PI.
I also use a PI to run a Dash Master Node. That PI also has piston so I can use it to run whatever script I need.
Both PIs have mosh-server so that my shell sessions resume whenever my laptop resumes from sleeping. That way I don't have to constantly log back in.
I also run tmux (multiplexor) from inside the mosh session so if I ever lose my mosh session, I can just reestablish a new session and pick up where I left off.
So I guess it's a little mundane. My PIs are basically just for ssh access. :D
I have an idea for something a little more diy. I want to set up a PI with a camera, looking at the road. I want to make it capture images of cars that go by and send them through a script to identify the cars using statistics. When it identifies a car, I'll have it run scripts to announce when certain people arrive.