There aren't very many actual dwarves that come up in the book, but only one is actually a well-known character.
Gimli, son of Gloin- He is a member of the fellowship, loyal and proud (as are all dwarves). He is stout and strong. He weilds an axe. Gimli's cousin, Balin, is the Lord of Moria. The fellowship finally went through Moria to head towards Mordor, and they found that Balin and his men were killed by the orcs.
Here is a quote from the book when Gimli was speaking to Galadriel (see Elf section), I think it reveals a lot about his character. It is when the fellowship was departing from Lothlorien and the Galadriel and Celeborn were giving the members of the fellowship gifts.
"'And what gift would a Dwarf ask of the Elves?' said Galadriel, turning to Gimli.
'None, Lady,' answered Gimli. 'It is enough for me to have seen the Lady of the Galadrim, and to have heard her gentle words.'
'Hear all ye Elves!' she cried to those about her. 'Let none say again that Dwarves are grasping and ungracious! Yet surely, Gimli son of Gloin, you desire something that I could give? Name it, I bid you! You shall not be the only guest without a gift.'
'There is nothing, Lady Galadriel,' said Gimli, bowing low and stammering. 'Nothing, unless it might be-- unless it is permitted to ask, nay, to name a single strand of your hair, which surpasses the gold of the earth as the stars surpass the gems of the mine. I do not ask for such a gift. But you commanded me to name my desire.'
The Elves stirred and murmured with astonishment, and Celeborn gazed at the Dwarf in wonder, but the Lady smiled. 'It is said that the skill of the Dwarves is in their hands rather than in their tongues,' she said; 'yet that is not true of Gimli. For none have ever made to me a request so bold and yet so courteous. And how shall I refuse, since I commanded him to speak? But tell me, what would you do with such a gift?'
'Treasure it, Lady,' he answered, 'in memory of your words to me at our first meeting. And if ever I return to the smthies of my home, it shall be set in imperishable crystal to be an heirloom of my house, and a pledge of good will between the Mountain and the Wood until the end of days.'
Then the Lady unbraided one of her long tresses, and cut off three golden hairs, and laid them in Gimli's hand. 'These words shall go with the gift,' she said. 'I do not foretell, for all foretelling is now vain: on the one hand lies darkness, and on the other only hope. But if hope should not fail, then I say to you, Gimli son of Gloin, that your hands shall flow with gold, and yet over you gold shall have no dominion.'"