The prologue of the LOTR gives the most information on Hobbit origins. These origins are lost in the mists of time, since Hobbits did not record them and Elves did not pay much attention to other races. At one point, Hobbit ancestors lived in the Vales of Anduin. Then numbers of them moved west.
Most interesting to me is that each branch of the Hobbits seems to have close ties to another race of Middle-earth, just like Feanor said. In the case of the Fallohides, they actually have some physical resemblance to the other races. The Harfoots, that came to be the dominant group of Hobbits, initially had much to do with Dwarves. They were browner and shorter. (I think Sam is Harfoot.) They moved westward earliest. Not surprisingly, with the Dwarf influence, they were the ones who came to live in tunnels and holes. The Stoors mixed more with Men; they came west later. They were the ones who liked boats, swimming, etc. since they lived by the river a long time. This was Smeagol's ancestry. The most intriguing to me were the Fallohides who were most like the Elves. They loved forests, were taller and slimmer, more adventurous, fairer of skin and hair, loved language and song, and in ancient times practiced hunting rather than agriculture.
The Fallohides provided many of the Hobbit leaders. Merry, Pippin, and Frodo all had Fallohide blood. I often wonder if some wandering Avari elf and some ancient Hobbit ancestor came together at least once to leave some special traits and genes for the Fallohides! We know Hobbit origin goes back before the Third Age.
No way to prove this. But it would go far towards explaining why Faramir can say that Frodo looks Elvish, and why Frodo is an Elf-friend and has visions of Elvenhome, or why Goldberry sees the light of an elf-lover in his eyes, or why he comments on his yearning for the sound of the Sea while in Rivendell. It would also place in context the last two lines of Galadriel's song to the departing Fellowship where she says "may you find Valinor". Tolkien explicitly says in The Road Goes Ever On that these two lines are addressed specifically to Frodo.
It could also be another reason for Sam's close emotional attachment to Frodo. Perhaps, like Faramir, he can sense some ancient throwback genes or traits. (You know how Sam likes Elves.)
Again, this is wild speculation. Maybe Frodo just likes Elves and Elvenhome, and there's no genetic component. That's certainly the case, for example, with Sam who has no Fallohide blood. And all the references to the Sea and the West could simply be preparing Frodo and us for the fact that he will have to go there for healing after the quest. But, then again, you never know...
For the nth time, I'm in no way saying that those I've posted are facts, they are just my wild speculations.
) But it would be strange not mentioning the hobbits.
...THAT thought has NEVER enterd my mind before...very interesting...