I used them as a sort of thin client into a system that I had root on, so I could do whatever Science demanded of me without asking for access. Permitted, but certainly unexpected!

I would carry a USB stick that just had a VNC client on it. My home server was built from high-end scrap, and was leagues faster than anything the department had at the time, at least for student use.

I also had a Sharp Zaurus I had jury-rigged WiFi into, so I could run data analysis whenever I thought of something. It ran VNC or SSH. This was in the early days before it was called "machine learning" or even "big data". So we take this sort of thing for granted now (hello Google Cloud), but at the time it was magic superpowers to have immediate access to a machine with 4 physical CPUs from a handheld device.