Can one die from pain?
I very much doubt it. You may however die from whatever's causing the pain. The reason you feel pain is so you stop doing whatever is causing the pain. Hence someone knows not to touch a hot fire because it is painful. But the pain itself is not actually the danger - it's the fire burning away skin. So pain is actually a good thing, a survival mechanism. So for something that is meant to prevent death it's hard to imagine it doing the opposite. 

Perhaps if you were in SO much pain you may be unable to breath and paralysed - but even then I still think you'd go unconscious before that would happen, and you'd start breathing again, etc.

The only other thing I can imagine is having a cardiac event, and the heart stopping. Again, this would be because of stress. Other than that - you may commit suicide on account of insufferable pain, however it's a different situation.

However pain never comes on its own for no reason, just like smoke needs a fire. In this case it's the fire - not the smoke, that will kill you!

People who've ever been in a desperate or life threatening situation like a car accident, have often walked on a broken leg for example - feeling no pain. In this case the body was giving them a chance to escape what might have been a lion, etc.

In short, no - I don't think you can. However I cannot give a 100% correct answer. It would take just one example to prove that however!