Iluvatar did. See below.

: Elves and men are the Children of Eru. Dwarves were created by
: Aule, and then given spirits by Eru. Yavanna did the same with
: ents. Orcs and trolls are degraded forms of elves (and
: possibly men) and ents. but who created the hobbits? Did the
: Professor ever say? Are they simply some variant form of man?
: I seem to recall reading a reference once to hobbits
: disappearing following the end of the Third Age, with some
: implication that they were assimilated into human populations.
: Is there an answer to these questions?

Okay, first of all, Orcs and Trolls are not degraded Elves and Ents. Orcs MAY have an Elvish strain but there is no clear statement attesting to this. Many people take the passage in THE SILMARILLION saying "yet this is held true by the wise of Eressea ..." as a definitive statement, but it's nothing more than report of a conclusion, a guess. In his later years Tolkien questioned the Elvish origin for Orcs and surmised the first Orcs must have been corrupted Maiar (of lesser power than, say, Sauron and the Balrogs, but still great power compared to Elves and Men) and that eventually they were blended with Men and, perhaps, some Elves. There are, of course, some difficulties with this point of view, but that is an entirely different discussion. :)

Treebeard said the Trolls were made in mockery of the Ents, not bred from them. Many people seem to confuse this definitive remark with the Elvish origin of Orcs surmise from THE SILMARILLION, inferring that he meant the Trolls were originally Ents. Stone Trolls were demonstrably not Ents -- Ents don't turn to stone. Other types of Trolls Tolkien felt had been bred from Men.

As for the origins of Hobbits, Tolkien did indeed say they were a branch of Men in one of his letters. I don't know anything about their becoming merged into the larger human population. That sounds like someone's speculation to me.

The Hobbits appear to have entered the Vales of Anduin late in the Second Age or early in the Third Age, and they stayed there only until the rising of Dol Guldur. We don't know where they came from but clearly they came from a land further east.

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Parma Endorion: Essays on Middle-earth, Revised Edition