Generally nothing that requires capable hardware, but benefits from a standardized computer that I can just flash an SD card image from my computer to deploy.
MQTT broker. Usually this does not require even a fraction of the processing power available in a RasPi.
AutoSSH. Why? So it sets up an SSH tunnel to a cloud VPS. Then I use a reverse tunnel to get terminal access to the Pi from the Internet, ignoring all firewalls / ISP NAT etc. I install this (with permission) in a client office or at home so that I can maintain local network services without driving to their office. Then they can unplug it when I'm done. This also uses only a tiny fraction of the RasPi's processing power, but the standardized hardware makes it easier to deploy (SD card image) and maintain.
Oh also it can probably run a Deliantra (http://www.deliantra.net/) server. That's a fun little game to play with some friends.