Pre-compiled binaries for PocketMine are available for the Raspberry Pi. PocketMine is essentially a Minecraft Pocket Edition server. Just like Minecraft, it has an API you can use. More information on PocketMine.

Here are the instructions from the Minecraft forum:

1. Use a newish version of Raspbian – one with the Hard Float stuff enabled.
2. Grab the stable or development release of PocketMine-MP from http://www.pocketmine.net/
3. Place the download in a folder. Run the Linux installer with the -u parameter to make sure PHP doesn’t get compiled.
4. Download the latest PHP_5.x.x_Raspbian_hard.tar from Sourceforge.
5. Extract the file into the folder where PocketMine-MP is located. The bin/ folder should be where PocketMine-MP.php is.
6. At the command line, do: chmod 0755 bin/php
7. Run ./start.sh in that folder and the server should start

Read the original post on the Minecraft discussion forum