9 times out of 10 this is a broken wire at the plug end, since that's under the most stress usually. What I did was order a dozen of these things:
http://www.amazon.de/gp/product/B003...ls_o01_s00_i00
They're basically like sacrificial anodes, their only job is to take the stress off the headphone cord. When one breaks I just throw it out and stick the next one on.
But sadly that won't help fix a broken pair. If it really is the plug end that's causing the problems you could cut it off and solder a new plug on, there's nothing to lose by trying at least. It might be a little tricky since most headphones have really thin wires coated in epoxy that has to be removed first, but I had some luck with it back in my college days when I was short on money. It wasn't pretty, but it worked
If it's the headphone end that's causing trouble you might even find that you only have to solder the wire back onto the speaker contact, that shouldn't be too tough after you get them open.