Remote wifi temperature sensor. I have an existing 1-wire temp sensor net & wanted to put something in the greenhouse w/o running a wire. I just needed to add a cheap wifi dongle and it just worked. I took a small $ risk and almost no time. If I was doing 10-20, there are cheaper solutions for more time spent, but I think I got a good value.
Since then, I played with RiscOS on it. I'm now playing with it as a thin client that someone built. I'm also going to play with Plex on it. Maybe I'll play with Plan 9 on it.
The first task could probably be done on on any of the other ARM boards that run Linux. The others tasks might work on other boards, but people are building and optimizing for the RPi.
All these ARM and microcontroller boards are fantastic. RPi made the others hit the under $40 price point. It reminds me of the days of Apple vs C64 vs Atari vs IBM and I hope they stick around.