Orcs are degenerate elves that were tainted with Evil™.
So yeah.
Among about five other "origin of orcs" - stories from Tolkien, yeah.
In my opinion, one cannot forget the Christian element. Only one figure (Sauron) can be said to be a font of nothing but evil, -snip-
You're forgetting Morgoth, the guy who tainted Sauron.
In any case, in Tolkien's stories, evil forces are incapable of creation - Morgoth/Sauron cannot have *created* orcs from scratch. That doesn't rule out the tainted elf theory, though. However, someone pointed out that if orcs are elves, even fallen, they still wind up in Halls of Mandos if they die.
Then again, *why* do orcs fight on the side of the bad guys? My assumption is that they're the easiest of races to corrupt with promises of wealth and power, and the bad guys simply have a more interesting offer. If they genuinely believe that the world will become a better place if Saruman and Sauron win, then they're just misguided. If they do it just for fun, there could be orcs having fun against Sauron and Saruman as well.