I vaguely recall that there is at least one species of predator that is basically immune to the quills, but I don't know what it is. Googling 'porcupine' will probably yield the answers after a bit of digging.
If you or a pet should find yourself on the receiving end of the quills, do not try to yard them out. They're hollow and filled with air. Cut them off an inch or two away from the skin to deflate them and then carefully wiggle the barbed end out. If left in, they cause a nasty infection.
Remember, as well, that porcupines can not 'shoot' their quills. You have to come into physical contact with the animal.