system
Given the following post, respond as if you're commenting on Reddit:
human
[LOTR] Can hobbits and humans breed?
gpt
Yes.

Hobbits are a race of men, therefore human.

Arguably 'Human' is a term that applies to both the Edain and the Eldar.  They are biologically the same species.  

The Edain includes High Men, Middle Men and all other forms of Edain, including Hobbits.  High Men are the Dunedain/Numenoreans, Middle Men are most other men in Middle Earth, possibly including Hobbits as they share a common heritage with the Rohirrim.

The Eldar include all elves and possible the Orc/Goblin subgroups depending on the source material.  The Silmarillion explicitly says that orcs are elves, but some discount that as an error.

In theory Men, Elves, Hobbits and Orcs are all the same species and thus could interbreed.  They don't do so for various political, religious and health and safety reasons, health and safety being emphasized when referring to Orcs.

Edit:

There is also a certain amount of racism with regard to interbreeding.  Elves and the Edain are not above intermarrying (and it's implied to occur quite a bit more than written about), but this is a privilege generally reserved for the higher lineages of men, such as the lords of men.  

Orcs and Goblins are discriminated against by pretty much every free race.  Though a peaceful orc is never shown, it's not outside of the realm of possibility.  Unfortunately a peaceful orc would find no quarter in any society.  Orcs would kill them for being a 'traitor' and the free people kill orcs indiscriminately.  So even if they were just mutilated elves there would never be an opportunity for an orc to have a meaningful relationship with an elf or man.  Rape can cause a child to be conceived (rape is a rare subject in Middle Earth literature), but if an orc (or anyone for that matter) were to rape an elf the elf would actually die due to the nature of their spirit.  A man would not die however in the case of rape by an orc, so they might be able have a hybrid child with an orc.  This is one of the possible sources of the Uruk-hai.

Hobbits do live by other men, especially in Bree, but intermarriage is never shown.  Hobbits tend to be a little clannish, so marrying one of the 'big folk' is probably socially unacceptable, even for the most cavalier or adventerous hobbit.