Several versions of the origin of Orcs exists. The wise of Eressea said they come from Melkor's experimentation on elves. Another version, also told by an elf, says that it is more likely that they come from the same experiments on men. Still another version suggests that the experiments were held on the Druadan, also known as Woses, Ghan-buri-ghan's people..
References: Lord of the Rings, Unfinished Tales
Oct. 1, 2001 addition:
In the Silmarillion, "Of the Coming of
Elves", the story
tells how Melkor, already in Middle-earth, was the first Vala to know
the awakening of the elves. Expecting Orome to find the elves while
riding Nahar, Melkor either sent out lying whispers or actual dark
riders to make the elves shun Orome in fear that he would eat them.
When Orome did come, the elves were afraid at first so that some ran
and hid and were lost. The courageous ones who stayed saw the light of
Aman in Orome's face and were drawn to him. But the unhappy ones who
were ensnared by Melkor were imprisoned in the pits of Utumno,
according to the wise of Eressea (elves):
"...and by slow arts of cruelty were corrupted and enslaved; and thus did Melkor breed the hideous race of the Orcs in envy and mockery of the elves, of whom they were afterwards the bitterest foes. For the Orcs had life and multiplied after the manner of the Children of Iluvatar; and naught that had life of its own, nor the semblance of life, could ever Melkor make since his rebellion in the Ainulindale before the Beginning; so say the wise. And deep in their dark hearts the Orcs loathed the Master whom they served in fear, the maker only of their misery. This it may be was the vilest deed of Melkor, and the most hateful to Iluvatar."
- "Of the Coming of the Elves", Silmarillion
July 5, 2007 addendum:
In the Silmarillion,
"Of the Sindar", the dwarves of Belegost warned the Sindarin King
Thingol of elvish kindred in the North fleeing from their homes in the
plains to the hills, in the land east of the mountains. There, evils of
the North not rooted out by the Valar, had multiplied in the dark and
were now roaming.
Later, evil creatures came to Beleriand from over the mountains or up from the south through dark forests. Some were wolves or creatures that walked in wolf-shape, other fell beings of shadow, and Orcs. At this time Thingol took thought for weapons, going at first to the same dwarves for this. From the dwarves, the Sindarin elves learned to make their own and, well-supplied, beat back all the creatures of evil and had peace. This power and peace attracted the Nandor to them for protection, as those folk had no weapons of steel against the fell creatures. The Sindar stored their new collecton of unrusting weapons and armor for the future, and it was well that they did.
Of these Orcs, the text says: