Grumpy_Mike:
That will not do. You need a current limiting circuit of some sort. Using no resistor does not change the peak current which will exceed the current capability of the Arduino pin.
Well, I see it done all the time. As far as an LED, what kills them is heat. An LED will withstand 10 times or more current than it's rated maximum in short pulses. A typical example is an IR remote emitter. The Vishay TSAL6400, for example, has an absolute maximum forward current rating of 100 mA, but the max PULSE current rating is 1.5 amperes.
In use as an IR remote emitter, the code data is burst out as millisecond length pulses at 50% duty cycle (i.e. the 40 kHz carrier freq). The pulses are only sent for a fraction of a second, then there is a long period (seconds to days) of time where the LED draws no current. Obviously, this isn't hurting the LED die... it's made to work that way.
As far as the AVR (or any other MCU) outputs are concerned, they are typically "totem pole" mosfets setup to both source and sink current. A mosfet appears as a resistor when it's turned on, and like the LED, the mosfet can be killed by heat (simply I squared R where I is the current and R is the on resistance of the mosfet).
The mosfet can be "grossly" overloaded for small pulse periods and suffer no ill effects, As long as the total power dissipation integrated over time NEVER exceeds what the mosfet can withstand, it will be fine.
Not only is it commonplace and perfectly fine to use an LED direct connected to an output pin, it's also done to make the LED seem to be brighter than it is.
(edit to add): Newer cars do this with their tail lights. The LED's are pulsed on and off at different duty cycles for "running" brightness and "brake light" brightness. And unfortunately, I can see flicker up to about 80 Hz. Old CRT computer monitors gave me headaches because they have a clearly visible (to me) flicker. Same with sodium street lamps. I can see the flicker. I can usually see a digital alarm clock scanning the individual digits. Looking out of the corner of my eye makes it even worse.
An LED at 100% duty cycle at "X" current will not appear as bright as an LED at 50% duty cycle at "2X" current.
Notice in the sentence above that the average power dissipated by the LED is exactly the same.
It may bother the sensibilities of a purist engineer not to use the series resistors, but in reality they are not needed.