Version 1.5.1.23735
GTVHacker found two ways to root the latest released firmware, resulting in boxeehacks.
Version 1.0.1.16319
This was the first firmware release by Boxee and they closed the holes from the first version (1.0.1.16216). They learned from the [[UnBoxed]] app and closed external command calls and they also removed telnetd from Busybox.
The instructions for obtaining root are located on the Obtaining Root on 1.0.1.16319 page.
Version 1.0.1.16126
This was the original version of the 1.0 firmware. This version of Boxee made it trivial to get root privileges. In this version they didn't prevent external command calls from within python and they also left telnetd compiled into Busybox.
You can get root by following the instructions in TelnetD.