The maximum USB current which I've always heard is 500 mA.
A capacitor will help it get through sudden voltage drops.
As far as I can tell, a computer manages the USB port for how much current is flowing. Occasionally I have plugged in a device (a portable hard drive, maybe) which brings up an error onscreen, saying "A device has drawn more power than this USB port can provide." Then the port shuts off.
I think I remember the message gives me a choice to reset the port. This allows me to unplug the device and try again.