How can I remove a stuck tub spigot?
This is what worked for me (it's rather brute force, but functional):


Take a small C-clamp (I had a 3" one laying around) and place it in the mouth of the spigot on the right hand side with the body of the clamp facing down. 
Tighten the clamp
Twist the clamp counter clockwise using the body of the clamp as a gripping surface and leverage
If it doesn't work try tapping the spigot with a hammer or mallet to jar it loose a bit then try the clamp again.


Note: this may damage the spigot a bit, it was useful to me as the spigot was already broken and all I had available was a hammer and a clamp.