I had the same problem when I was restoring my (then recently
Ebay purchased) bicycle about a year ago. I tried everything I could think of, including heating with a blow torch and clobbering with a hammer, all to no avail. The bike seemed to have been stored in damp and possibly salty conditions for some years, and the pedals had welded themselves permanently to the cranks.
A little lateral thinking eventually solved the problem, though. I dismantled the existing pedals, leaving only the 'axle' part in place, then built new pedals onto the existing axle (not sure if this is the correct term for the part that runs through the middle of the pedal and is attached to the crank) using parts from a newly-purchased pedal set. Although this procedure did involve fiddling around with ball-bearings, grease, and suchlike, it was a complete success, was interesting, and I have since done several thousand miles on the re-built pedals with no problems. I don't mind spending time on this sort of thing so long as I learn something from the experience.
I'm not sure to what degree pedal parts are standardised, but the first set of pedals I purchased fitted the existing axles perfectly.
Steve