I'm assuming that automatically running software on the Raspberry Pi without a keyboard and TV at boot up is simple. My knowledge of Linux admin has faded over the years but I remember it could be done from /etc/init.rc or similar.
I specifically imagining hobbyists / children creating software on the R-Pi to do stuff automatically. For instance, a child sets up a Pi and USB webcam in there bedroom to time-lapse photograph a plant on the windowsill. They can leave it for a few days (or weeks) and at the end 'glue' all the images together to create a movie.
Similarly, they could use a battery powered Pi to test sensors and control motors on a robotic base.
I'm sure these ideas have been discussed already so I'd happily like some links to proposed projects.