When pedals with hex sockets in their butts get stuck, with too much force it is possible to crack the sides of the hex socket. Once this happens, the pedal becomes absolutely unremovable. You will have to throw out the crank and the pedal. (Unless you drill out the pedal spindle and somehow repair the thread, which is typically not worth it.)

This is something you have to keep in mind. There are lots of bad and inexperienced advice in this thread stating that all you supposedly need is "greater mechanical advantage". Ignore this advice at all costs. If your pedal is really stuck, the only thing you will achieve by applying excessive force to such hex socket is six cracks in six corners of the socket. This will be a total loss.

If you feel that the force becomes excessive (and the hex socket is stil intact), try warming up the crank and applying some penetrating oil. If this does not help, you will have to sacrifice the pedal: cut the outside portion off, leaving enough of the spindle sticking out. File the sticking out portion into something that will engage with a different kind of wrench (like open wrench). Some people use a saw to cut a slit for a hefty screwdriver. (And so on: use your imagination.) By using the outer end of the spindle you will be able to apply massive amount of force without the danger of cracking the hex socket.

If this does not work, throw out the crank. Next time apply anti-seize compound to the threads and unmount-remount your pedals periodically (re-applying the compound).