Really depends on the current draw. I powered a Duemilanove and 4 MAX7219s from 9V, it would overheat and shut down, cool off, restart, overheat, shutdown.
Switched to 7.5V supply and had no problems.
This video is USB powered, took it to work show off, with 9V for the barrel jack, had to switch to 7.5V the next day.
