I'm planning to connect 2 LEDs directly to my Pi 3's GPIO pins using only the LEDs and a 330 Ohm resistor. Can I accomplish this task without damaging my Pi?
I don't want to use a breadboard or any other PCB for this simple circuit.
Yes, you can connect the LED safely between any GPIO pin that is set for output and the ground pin. For something like this I recommend a setup where you do this for each LED you are adding:
You now have an LED that is short-hardened with two wires coming off the bottom. A nice neat package.
Use whatever app you want to set/unset the GPIO output voltage high/low to switch on/off the LED.
Good luck! I hope this helps!