Psion makes some small computers that could be categorized as PDA's. The Psion 3 runs EpocOs? 16 and 5 runs EpocOs? 32. Some newer model runs SymbianOs. The processor is a 36MHz ARM. There is a CompactFlash? card slot for backup and expansion, IR port and a serial port (with special cable).
There are clones, such as the Ericsson MC218 (5 clone).
There are some funny features in these. They (at least the MC218 I have) slide open revealing a mostly-complete keyboard and a wide LCD touchscreen. The screen is 640x240 pixels and 16 shades of gray in the MC218 and possibly slightly different in other models. It is touch sensitive and there is a stylus that is used as a pointing device. The touch-sensitive area is slightly larger than the display and there are "buttons" marked along two edges of the screen containing a set of common launchers and a few menu shortcuts such as zoom, infrared send/receive and clipboard (which all should ideally work and work the same way in all applications).
The whole package draws about 50mA to 100mA of about 2.5V (2 AA batteries and a CR2032 Li backup battery) according to the battery meter. Turned off, it appears to use virtually none (batteries' internal resistances drain them faster).
The system software includes a few PDA-ish things and a Basic-like language interpreter that presumably has bindings for most OS features.
You can find ports of B Prolog and Hugs Haskell interpreters at least and a very functional PDF reader, PDF+. There is a software suite to use on "real" computers called plptools and a file converter library calles psiconv available. Apparently some models are also able to run Debian Gnu/Linux (LinuxOs).
With the low power draw, wide screen and instant on/off ("suspend"), no moving parts etc, these can be quite convenient.