Q:

Power LED from 3.3V Power Pin without Resistor

I tried wiring one white LED to the 3.3V pin on a Pi Zero W with a 330 Ohm resistor but it's not as bright as I would like. If I wire it up without a resister I get a good amount of brightness. Is that a viable solution? Or should I try a smaller resistor?
If it matters, the power supply is a standard 5V 2.5A supply like this one. The LED is this one.

A:

You need to consider that the forward voltage of a white LED is likely in the range of 3.0 V to 3.2 V (according to the linked article). Assuming the best case of 3.0 V and a resistor of 330 Ohms and using Ohm's law R = U / I we find that the current is about 1 mA and thus the brightness of the LED is rather low. Decreasing the resistor will help to some degree but be aware that this is borderline in any case. Say 33 Ohms will get you about 10 mA which might be ok. Best bet is to use the 5 V instead and design the resistor in such a fashion that the current suits the safe operational range of the LED. 
Connecting a LED to a voltage source without a current limiting resistor is not a safe way of operating a LED. It is therefore not advisable to do so.
Find a more elaborate description of the calculations here; even though it is aiming at GPIO pins the physics still apply.

