First off, I am NOT an electrician, so this is my own personal $0.02.
It sounds as if you may have a detached neutral wire. The electric current flows from the hot leg, through your device (lamp, fan, radio, tv, etc.) back through the neutral.
Voltage drop is caused by the current times the resistance (OHMs law V=I*R).
If the neutral were disconnected, there would be no path for the current to flow. Therefore the neutral leg will "float" to the same voltage as the hot leg.
Lots of comments here in previous posts that will tell you that having a loose/detached neutral is a very BAD thing.
I'll let others chime in to see what they have to say on the subject.