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.