I am a beginner playing with an IR LED. I have a sketch turning pin 13 on and off again in a loop. I can see this working as the on-board tiny LED on the arduino turns on and off as expected. I then connect my IR LED (Salvaged from a remote control) to pin 13 and ground. I expect the IR LED to turn on and off like the on board LED. Looking through my camera, I can see that the IR LED is on all the time. It does not turn on and off?? Also, the on-board LED stays off?
Your "impression" is just an impression. There had been some old boards (serial, I think) with such a resistor, indeed. For your specific Arduino please look at the specific schematic.
Especially blue LEDs work fine without any resistor. They force the Arduini output down to 3.5 Volts and upto 40 mA current . This is stress for both, and the question is just who will give up first. Pulsing them with a duty cycle of 50% will reduce that stress considerably. Red LEDs schould however break soon....
There is a lot of IR LED kinds, some accept quite a high current typically above 100mA. There is no chance for the Arduino to deliver this, so this works like a shortcut. In this case it's not the LED that will break but the Arduino output.