It's only 20 degrees outside. The only faucet that isn't working is our basement shower. All other faucets are working and running water. I have set up a heat dish in that bathroom and left the faucet on. There seems to be some water dripping from the shower head, although not much or constant. Should I do anything else? Could it be a frozen pipe?

Check by-pass valve(s) position on back of tank.

Water pipes throughout yoru house need to be drained, this is assuming that the water is actually turned fully off. Also, turn off the hot water tank, as sometimes that keeps expanding and pushing water. Open faucets in the basement and on the top floor to facilitate draining.

If I understand correctly, you have single handled shower faucet.
Normally there is a wait for hot water to arrive at faucet.
But now hot water is already at shower faucet.

Single handled faucets have a mixing area inside valve where hot and cold come together before going into sink.
This mixing valve can have crossover where the hot and cold can pass through to each other even when faucet handle is off. When single handle faucets get old, this can happen.
How it happens:
For example another faucet is turned on inside house, and pressure differential between hot and cold causes hot water at shower handle to pass through mixing area and into cold water line.
So if another faucet has been run, then that lets hot flow to faulty single handled shower faucet.
To confirm this is the problem: turn on other faucet and put ear against shower faucet to listen for moving water.
This condition may also signal there is a water leak.
The problem is not harmful, but will draw cold water into water heater each time, and is energy wasteful.
Replace faucet or have plumber repair problem.

It is air in the line. I had the same problem. To solve it you need to find the main water valve in your house, usually in the basement, and shut it off. Then go to the faucet that is giving you the problem and turn on both hot and cold and let them run for a few minutes until there is no water coming out. Leave the faucets turned on and then go back to the main valve and turn it back on. You will hear sputtering noises as the water starts coming back through. Let it run for a few minutes. I had to do it a couple of times to get all of the air out. if that is not working, then you should try to do the same thing, but also open and drain the lowest faucet in your house, like in the basement. Hope that helps. It worked for me. <!-- from fixya rte -->

Sounds like diverter valve which is your shower handle valve is bad take it apart and check out and replace it if possible because that transfer water to shower head.

Hello. It sounds like your plumbing was installed wrong, with the hot and the cold supply lines reversed. If that is the case, those supply lines will have to be replumbed to make your faucet work properly. Often, if those lines are accessable, it is only a 20 minute job. Joe

Most likely bad solder joint or leak where shower arm is screwed into fitting.

sometimes there are orings or gaskets that get tore in assembly one of those may be bad,or if it is around the threds you might try wraping teflon tape around the thred once or twice.hope this helps

Obviously your plumber when they were building the home hooked up hot water lines to both faucets and never hooked up a cold water line.

tun off the water.
unscrew teh allen screw under neath the handle. pull out hteh handle. undo the wall plate and gain access to the cartridge in the handle body. turn the artridge around 180 degree and reisntall all parts.