We know that we need to care for the AVR output pin current limit, the LED current limit and also to consider long term effects from abuse (rather than base our conclusion on a single limited scope test). This is a healthy base for discussion and a lot better than the opinionated "do as I say" posts. The question remains if we can design for these limits without a series resistor?
Looking at the Mega VI curves from the datasheet, we can extrapolate static on state resistance for the CMOS output stage high-side (source) and low-side (sink) respectively (5V @ 25C).
Sink resistance: 29 Ohms
Source resistance: 37 Ohms
1. If we short an output pin to ground, max static current will be limited to about 135mA (5V / 37) through the high-side output FET. This is less than the 200mA rail max for the chip total and so it is to be expected that the IO pin will have time to burn out before the chip resets. This is why we need current limiting on the IO pin as the AtMega is not capable of restricting current to safe levels.
2. If we short a 5V power rail to an output low IO pin, about 172mA (5V / 29) will pass through the low-side output FET. This again is way above max and so current limiting is required.
3. If we short two output pins (one high and one low), current will pass through the high-side FET on one pin and the low-side FET on the other pin. In this case, max current is about 76mA (5V / (29 + 37)). This is less than the single pin sink/source cases, but still a guaranteed failure.
A LED follows a sharp VI knee- curve where current is allowed to flow freely above its forward voltage, but blocked below this same voltage. Because of this sharp knee-curve, we need to limit current as soon as we exceed the LED forward voltage. Typically, we add a series resistor in this case such that the voltage drop across this resistor plus the forward LED voltage drop match supply voltage for a given target current. The formula for this relationship is as follows:
I = (Vcc - Vf) / R
A broad spectrum (white) LED will have a typical Vf of 3.5V whereas a red LED will have a Vf of about 2V only. If we apply the above formula and substitute R with the AtMega output stage resistance, we can calculate Vcc so that current (I) stay within limits for a given LED forward voltage (Vf).
For a white LED and case 3 above, we would need to limit Vcc to about 4.72V for a target current of 20mA. Max current at 5V would be about 22.7mA for this LED without a series resistor.
For a red LED and case 1 above, Vcc would have to be as low as 2.74V for a current of 20mA. At 5V, current will exceed 80mA. At 3.3V, current is about 32 mA.
Does this mean we can eliminate current limiting series resistors for LED's in general? No, we always need to consider current limiting. Output stage resistance however may be all that is required for some designs (such as white LED's @5V or other LED's at 3.3V). Is it not better to just always use an external series resistor? Well, that is for you to decide.