File system full on Slave (no replies)

I checked my servers this morning and found that my slave's /var/lib/mysql file system was full. When I run `show slave status` on the server, I see the following error:
Slave_IO_State: Reconnecting after a failed master event read
I can't get a mysql prompt on the slave server because the file system is full.

What can I do? What files can I remove or move so I can purge some BIN files? Can I just delete the BIN files to make some space?