I was playing LOTR War in the North the other day. Despite its inaccuracy, there was one part where I had to fight a stone giant. I don't recall this from any of the books I've read, which are numerous. So I would like to know.
Where did giants come from? Are they Maia spirits like those of the Eagles and Ents? Do they originate from Melkor (Morgoth)?
Giants occur in several of Tolkien’s works, but we never learn a great deal about them. Lúthien’s sleep-spell, already cited in reference to the beards of the dwarves (see p. 77), invokes ‘the neck of Gilim the giant’ and ‘the sword of Nan’ (BLT II.19) in its list of the longest things in the world, but little is known of either of these figures beyond the names.
The History of the Hobbit
In Tolkien's earlier works, he prominently features Giants, from Gilim mentioned above, to the giant who wanders Little Kingdom only to run into Farmer Giles. However, in his most famous work, Lord of the Rings (LR), Tolkien never had time for giants. Although the inclusion of creatures such as Trolls and Ents certainly suggests the possibility of the existence of "giants" in LR.
In early manuscripts, giants were certainly counted amongst the agents of Melkor:
At this point in the story the agents of Melko appear, the Úvanimor, ‘bred in the earth’ by him (Úvanimor, ‘who are monsters, giants, and ogres’, have been mentioned in an earlier tale, p. 75); and Túvo protected Men and Elves from them and from ‘evil fays’.
The Book of Lost Tales, Part 1
However, in the Parma Eldalamberon XIV it is mentioned that giants were later considered amongst Men.
Giants are clearly more prominent in early version of the Legendarium, however with the dissipation of the creatures, not much is known about them in the final, published works of Tolkien (at least during his life), their origins, however, are never made clear beyond them either being agents of Melkor or possibly men.
The stone giants from The Hobbit are discussed in this question.
To add to Edlothiad's answer, there is another giant mentioned in some of Tolkien's later works, written c.1967.
Tolkien was putting together a guide to translators of The Lord of the Rings, and he was explaining the origin of many of the place names to help guide whether they should be translated or left as is.
For Tarlang’s Neck (a pass in the white mountains that Aragorn and the Grey Company travel through), Tolkien had drafted out a legend involving a giant named Tarlang.
... Tarlang in local legend was the name of a giant of ‘long ago’ of one of the giants who in ‘ancient days’ had built the White Mountains as a wall to keep Men out of their land by the Sea. But Tarlang, while carrying a load of rock on his head, tripped and fell, and the other giants used him to finish the wall at that point, leaving his neck lying southward, while his head and the load made up the Sjouthern] mts of the ridge, [?called] Tarlangs, that separate the plain of Erech from [?Lamedon],
The Lord of the Rings: A Reader's Companion - Book V, Chapter 2
He then rewrote this note to be more descriptive:
... But owing to the facts that lang ‘neck’, though frequently used geographically, was also applied to the neck of men and animals, while Tarlang was a not uncommon man’s name*, there grew up a local legend to explain the name. It was said that when ‘in ancient days’ some giants were building the White Mountains as a wall to keep Men out of their land by the Sea, one of them called Tarlang tripped and fell on his face and as he was carrying a heavy load of rocks on his head he broke his neck and was killed. The other giants used his body to complete the wall at that point, but left his neck lying southward, leading to the three mountains of the spur: Dol Tarlang ‘Tarlang’s Head’, Cûl Veleg ‘Bigload’ and Cûl Bin ‘Little Load’. The break in his neck was shown by a depression in the ridge, near the junction with Tarlang’s Head, over which the road went.
The Lord of the Rings: A Reader's Companion - Book V, Chapter 2
I believe this is the most extensive reference to a giant in any of Tolkien's written work after The Hobbit.
