the origin of hobbits

[Meneltarmacil]

To me, Hobbits seem like a combination of Elves, Dwarves, and Men.
MEN: Their ability to adapt to a number of different situations quickly, their will to survive
DWARVES: Their short stature and the fact that they live in holes
ELVES: Not as apparent as the others, but Bilbo and Frodo seem to show some elven traits.

So what I think happened (and this is just my opinion) is that somewhere, possibly in the Far East (Avari Elves, Men of Hildorien, there may have been some dwarves in the Orocarni), all three races intermarried and Hobbits were the result after many generations.

Oh, and as to my idea above that there were dwarves in the Orocarni, the Silmarillion says that Aule put them in "far sundered places" and gives no real specifics other than Moria, so it is possible.