Dr. Scott M. Baker has designed and built a PoE-powered lab power supply using a DPS5005 and custom PoE board:
The DPS5005 is a DC-DC converter. It can accept an input voltage from 0 to about 55 volts or so, and will regulate an output voltage up to about 1 volt below the input. This version is good to 5 amps, but there are other versions of this supply that will do as little as 30V / 2A and as much as 50V / 20A. 50V 5A seems like a good sweet spot. Since it is a DC-DC converter, you have to have a DC source to drive it. A lot of people use a 48V power brick, as they are commonly available.
Project info at smbaker.com.
Check out the video after the break.