Up to 800mA thru the 5V regulator with a low voltage source, as DVDdoug says.
http://www.dipmicro.com/store/DCA-07510
Above that voltage, you need to worry about overheating.
Out of that 800, the Mega 2560 uC uses some, the USB/Serial uses some, the 3.3V regulator uses some, whatever IO you are driving uses some ...
So probably on the order of 700mA if you have little to no IO using energy.
If powering from the USB port, the starting number is 500mA, limited by USB port and the onboard 500mA PTC resettable fuse.