Dwarves
This is covered in Silmarillion Chapter 2, Of Aule and Yavanna:
Aforetime it was held among the Elves in Middle-earth that dying the Dwarves returned to the earth and the stone of which they were made; yet that is not their own belief. For they say that Aule the Maker, whom they call Mahal, cares for them, and gathers them to Mandos in halls set apart; and that he declared to their Fathers of old that Iluvatar will hallow them and give them a place among the Children in the End. Then their part shall be to serve Aule and to aid him in the remaking of Arda after the Last Battle.
Hobbits
The question of Hobbit origins has previously been answered: Hobbits are a variety of Men, and as such will share the same fate.
Ents
The fate of Ents is not stated directly, but Entish origins are given in the Silmarillion (Of Aule and Yavanna again):
...the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared.
Tolkien never really said what these "spirits from afar" actually were. They're evidently nature-spirits of some kind (Bombadil may even be one, Goldberry almost certainly is one), but are they Maiar or some other class of spirit? In the end we don't know.
However, Ents do appear to be immortal within Arda, as per Galadriel's words to Treebeard in RotK:
Not in Middle-earth, nor until the lands that lie under the wave are lifted up again. Then in the willowmeads of Tasarinan we may meet in the Spring. Farewell!
This is a reference to the End of the World and to Arda Unmarred, which requires some discussion of the Second Prophecy of Mandos to fully elaborate on, and as such is outside the scope of this question.
Orcs and Uruk-hai
I'm taking these together because they have the same origin ("Uruk" is just Black Speech for "Orc" after all). It seems obvious that the fate of Orcs depends on this origin; but unfortunately Tolkien never finalised it satisfactorily (there are serious chronology problems with his decision that Orcs have a Mannish origin). We may assume that if Orcs were Elvish they'd go to Mandos but never be released, if Mannish they die and leave the world, etc.
Maiar and Balrogs
Again, I'm taking these together because Balrogs are Maiar. As they are both Ainur who came into the world at its creation, their spirits are bound to the world until its end. This is said in the Ainulindale of the Valar, but since the Maiar are of the same order of beings (just of lesser might) the same applies:
...their power should thenceforward be contained and bounded in the World, to be within it for ever, until it is complete, so that they are its life and it is theirs.
However it is possible for Maiar to die and leave the world: this happened to Gandalf, after all:
Then darkness took me; and I strayed out of thought and time, and I wandered far on
roads that I will not tell.
Letter 156 is confirmation of this:
'Naked I was sent back – for a brief time, until my task is done'. Sent back by whom, and whence? Not by the 'gods' whose business is only with this embodied world and its time; for he passed 'out of thought and time'.
In Tolkien being "immortal" means being bound to the world until the End of Time, whereas being "mortal" means that one's spirit leaves the world. However, Gandalf, as one of the Istari, was bound to a mortal body and the same applies to Saruman. We also have cases where fallen Ainur (Sauron and Melkor) are bound into their "Dark Lord" forms, so we can assume that this also applies to Balrogs.
A Maia who is not so bound can be slain, but it's only their form that is destroyed; their spirit lives on in Arda and can make a new form for itself. This is what actually happened to Sauron following the Fall of Numenor (see the Akallabeth):
But Sauron was not of mortal flesh, and though he was robbed now of that shape in which he had wrought so great an evil, so that he could never again appear fair to the eyes of Men, yet his spirit arose out of the deep and passed as a shadow and a black wind over the sea, and came back to Middle-earth and to Mordor that was his home. There he took up again his great Ring in Barad-dur, and dwelt there, dark and silent, until he wrought himself a new guise.....
Melkor
I'm adding Melkor because at the end of the First Age he was actually executed by the Valar; in the Silmarillion we learn that:
But Morgoth himself the Valar thrust through the Door of Night beyond the Walls of the World, into the Timeless Void; and a guard is set for ever on those walls, and Earendil keeps watch upon the ramparts of the sky.
Referring to Gandalf's "out of thought and time" above, it is obvious that "the Timeless Void" means the same thing. It's also obvious that even there, Iluvatar can intervene if he wants to: he did with Gandalf, he presumably wouldn't with Melkor.
