Pin 13: Do I need a Resistor?

If you examine the schematics for any of the Arduino boards (other than the Arduino NG Revision C, which does not have an on-board user LED), e.g. the one for the Arduino Uno, the pin has a resistor and then the LED wired off it to ground, in parallel to the actual output pin header.

Thus, if you do not use a separate resistor in series to your own LED, there is a fair chance of damaging your LED.

Thus, yes you do need a resistor for your external LED.

Only the very early boards had a resistor on pin 13. The numerous tutorials out that there that still claim pin 13 has a resistor are just flat out wrong. No recent (well over 2 years now) Arduino has a built-in resistor on Pin 13.

Question-in-short: Do I need a current-limiting resistor when using pin 13 for a (small) LED?

ALL LEDs, regardless of size, require some form of current limiting. When the forward voltage of the LED is applied, it turns into a short circuit. A LED only drops its forward voltage. So if the forward voltage is 3volts and the I/O pin or supply provides 5volts, something else needs to drop the remaining 2volts.

A series resistor will drop the rest of the supply (or pin) voltage and limit the current running through the LED.

For higher power LEDs you would probably want to use a constant current supply so that the series resistor isn't just wasting power.