If your servos are put under a load that is greater than they can handle, they can be damaged by drawing too much current. To prevent an over current situation from damaging your servo, you could put a fuse inline with it's supply or ground connection, so that if the servo draws too much current, the fuse will blow, preventing damage.
One annoyance of this setup is that the fuse must be replaced if it is blown. To avoid this inconvenience, you could use what is called a PTC fuse, which unlike a normal fuse, resets after power is removed.