Two switches, one controls both
Well, look at the simple diagram below:



If one switch is stuck then the other will complete the on/off function, but if one of the parallel wires is broken then the symptoms will be similar. A multimeter to test what is happening would be my next move.

As my simple diagram seems to confuse people, here is a picture taken from this source which shows a similar circuit, but this only needs a single wire to go between the two switches...:



(source: Light Wiring Diagrams)