JoeN:
This document says the 74HC164 can source 25mA per pin or sink 20mA per pin and dissipate 750mW per package. I would say it is perfectly fine to drive normal LEDs on such an IC. Limit current to 20mA with resistors.
That datasheet also says: Icc - DC Supply Current, VCC and GND Pins - 50mA
ie. You can't source 20mA on more than 2 pins at the same time.