I need to run power to a new outlet in a closet for some internet gear (cable modem, small switch, etc.).
The closest power is on the opposite of the same wall at the power switches for a bathroom light and exhaust fan. Can I just wire my outlet to the hot and neutral in that gang box?
I know it will work but is there any reason I shouldn’t do it?
And ground, don’t forget ground.
The biggest risk is that you network is now a function of your bathroom lighting 
Most jurisdictions have additional requirements for bathroom circuits, but this should not effect you.
You might be tapping downstream from a Ground Fault/Arc Fault outlet or breaker. Some wall wart supplies can make these unhappy, but that’s unlikely.
Just make sure you aren’t exceeding the circuit rating. Most residential networking gear presents an insignificant load. Bathroom fans with heaters can run right up against the limit with a light or two on.
What you’re suggesting should work fine as long as the added amps plus what is already on the circuit don’t exceed the breaker limit. As stated you need to make sure you wire the ground, too. Essentially you’re just adding an extension cord permanently.
As stated a GFI in the circuit can be problematic if it is tripped. Whatever is on the circuit will lose power until it is reset.
I’m not an electrician but my dad was and I assure you I’ve wired a lot of circuits with him.
Master electrician here. Everything they said above applies. However, the bathroom fan has a motor it could present some disturbance on the IT circuit, but probably not, or if it does, most likely it would be minimal. But there is always some potential risk for it when dealing with motors, albeit minimal in this case. If you do tap from the GFCI receptacle instead, you can tap power from the wires that feed the line side of the GFCI receptacle so that you are not downstream from it. That way if the GFCI trips, it won’t affect your IT gear. Again, depending what you plug in here, there could be some minimal risk for interference on the IT circuit, but probably minimal. Depending when the house was built, the bathroom might be on its own circuit, or could be tied to other areas of the house. New houses are built to a new code requiring the bathrooms have their own circuit. Could be an issue if you have a new house and go to sell it, and the home inspector has issue with it. Not sure, never sold my house, but have heard stories of code issues being a problem with home inspectors. Main thing is be safe. make sure any connections are tight. Turn the power off before working on it. If you have any sensitive IT equipment, consider a dedicated circuit.
Thanks. I got it done. I bought bigger wire nuts for neutral and ground and I tied hot in by screwing, not backstabbing.
I think there is enough capacitance in my various power supplies to account for bathroom fan noise on the line. Nothing seems to care so far.
Thanks, guys!