In my LED build they are connected to digital pins, illuminated with analogWrite(3,x) where x is a loop-generated PWM value between 0 and 150. When I meter it on my bench Agilent the mA peak never exceeds 16mA. So, is a resistor required in this case?
FWIW - The same LED when metered on analogWrite(3,255) pulls 57mA. That's bad news I think; however, except for botched code it won't happen in the actual routine.