[inspired by a Michael Moorcock essay on the success of the nursery-rhyme motif in the fantasy genre, found here]
Orcs are the working class. The Tory vision of the working class, at any rate.
While hobbits and Men and Elves and Dwarves all come from storied ancestry and can recount the names of their forefathers and the grand halls (or grand burrows) from which they hailed, Orcs have no fathers. Orcs have few names, and of course the Black Tongue is nasty, brutish, full of short, sharp sounds.
Orcs toil; we never see the Free Peoples toiling, except for a bit of farming now and again.
Orcs build. Orcs make engines that spurt flame; Orcs raze whole forests and dig deep, disgusting pits where they breed! Orcs, ironically, are the only race of Middle Earth whose breeding habits are put (mostly) on display; they are the only race that is growing, that is rising, that is gaining in strength. All around them are declining princes and listless civilizations. The Orcs have plenty of room to expand, and their industrial masters are happy to oblige.
Now, on the one hand there are a great many literary devices wrapped up in Orcs that make them easy to dislike, especially in the films: they're smelly, slimy, cannibalistic, unpredictably violent, and vaguely simian. Tolkien, at once, rolls dark skin, primate features, and spontaneous generation (they apparently "grow" in pits and come forth fully muscled and fully grown) into an altogether unpleasing whole.
At the same time, many fans of the trilogy find a certain pleasure in Orcs: they are dangerous, they are serious, they wear the coolest/scariest outfits, and they hang out with Wizards who do more than light fireworks and talk to bugs.
But again, Orcs are Tolkien's very Tory image of the working class. They're a dark-skinned, foreign-tongued horde of builders and soldiers and ruiners who eat anything and everything, are a threat to all (even themselves), and, most tellingly, are constantly under the yoke of powerful, singular demagogue intellectuals who dwell in not-quite-literal Ivory Towers.
Compare that to the Istari, who are angels in the shape of old men (a creative choice I can't recall seeing anywhere else but in It's a Wonderful Life). One Istari in particular is deeply fascinated by the middle-class, status-obsessed Hobbits of the Shire, and seems to like nothing better than spending time in their twee, half-size pavilions and houses and so forth.
The Orcs come to despoil the natural world, and cannot stop themselves. Their actions are not truly their own; truly, Tolkien's chief Enemy is the future, industrialization, science; Orcs, not being exactly scientists (beyond an offhand comment that they "made many clever things, but no beautiful ones"), are nonetheless the Industrial Army, ready and willing to build, destroy, and kill in the name of hated Progress.
While pretty much every major character among the Free Peoples is the descendant of some king, the Orcs, as I said, breed in holes in the earth. Ironically, Tolkien has painted us a world where dark-skinned, violent humanoids would probably be called Mudbloods if the opportunity came up, and in which the Wizards must save us all from the dangerous, disgusting creatures of the earth that seemingly live only to breed and to build. Old men in hats will save us from those dirty workers, wot wot?