Pretty simple: we saw the armies of Men, and of Elves, and of Orcs, and of Trolls, and of Ents, and of Uruk-Hai. But no Dwarves. Now I know that many were killed a Moria, but I also know that there were other kingdoms - there were Dwarven armies in The Hobbit!
So, what happened to the Dwarves? Don’t they feel the need to help the other races, or are they really that misanthropic/miselfthropic?
In the book it is mentioned that the Dwarves of the lonely mountain and the kingdom of dale fought an army of orcs, both King Brand of Dale and King Thrain died in the fight. BTW if you meant the last alliance when you mentioned the armies of elves then its worth mentioning the Dwarves helped out in that war too.
From the Tale of Years (otherwise known as Appendix B):
So it’s more that the role they played was so small as to be footnoted, rather than nonexistant?
And although it didn’t show it, you say that there were Dwarves fighting against Sauron alongside Isildur?
Well, contrary to the movies, the Elves basically played no part in the central battles in the Mark, Gondor and Mordor. They were pretty well pent up in the north and west (not the West!) with their own problems, courtesy of Sauron’s minions. Galadriel and Celeborn did manage to lay bare the dungeons of Dol Guldur in the Mirkwood and cleanse that forest of Darkness.
Um…that was meant as a comment on the fact that, other than Hobbits, the forces of Light in the south were almost entirely human. None of the non-human Free Peoples had a huge military role to play in the waning days of the Third Age. Appropriate, really…their time was ending.
Another question - what happened to the Dwarves after the Elves left? Did they just go back to sleep? Or die out?
Probably they slowly dwindled, carrying on in out-of-the-way locales, until finally the ascendancy of man caused them to just give it up as a bad job.
I don’t think JRRT said too much about their fate in middle-earth beyond that.
But weren’t they supposed to be around for the rebuilding of the world? Or do they go to Mandos like the Elves?
They died out. The Dwarves were already declining. Their male:female ratio was badly skewed, and many of the few females never married. So their rate of replacement was low, and they’d been in a fierce series of wars with the orcs and dragons of the various mountain ranges for millennia.
That’s part of what made the Dwarves such a dour race. They were well aware that they were doomed.
The fate of the Dwarves after death is something of a mystery. The Elves had generally claimed that the Dwarves did not go to Mandos. The Dwarves argued differently, that they did go to the Halls and were released at the last battle to fight beside their maker Aule.
I’m at least somewhat sympathetic to the Dwarven side here, considering that the Elves haven’t exactly had the most civil relations with them.
Well, the Avari did think the dwarves were a version of Orcs when they first appeared, and hunted them quite a bit. Got some bad blood flowing from that.
That was pretty much what I was talking about, QtM. 
Well, that and the whole Nauglamir mess…
It’s not that the Battle of Dale was small (in relation to the forces available to the dwarves in Erebor, that is). It’s just that it took place far away from the story being told.
In the Last Alliance of Elves and Men at the end of the Second Age, both men and dwarves could be found on both sides. Many dwarves also remained neutral. But at least some of the dwarves of Durin’s line fought against Sauron.
jayjay, I was speaking up in support of your statement. Of course it would help if I made clear just what I was trying to do when I did it. 
In JRRT’s early dwarf tales, they were an evil race, led by the dwarf Fankil, servant of Melko. The tale “The Nauglafring” really doesn’t make them look nice at all. No, not at all! Fortunately JRRT re-invented them.
What happened to the hobbits?Did they dwindle too?
It’s implied in the prologue that Hobbits are still around but rarely seen.
I’ve heard it said that Hobbits are in fact just diminuitive Men. If this is true, then that means they could have just integrated over the millennia of the Fourth Age. Right?
Speaker for the Dead you are absolutely correct on that score. My wife and I are descended from hobbits–meet the physical description (well, add a foot in height) and, before we ever discussed it, both shared an aversion to the physical appearance of anyone over 5’ tall no matter how “attractive” they may be. And unambitious? Shucks, gimme a Ring of Power…the dang thing will have fits trying to get a grip on my soul let alone getting me to try & ‘wield’ it.