The Hobbit features a band of dwarves led by Thorin. They were Nori, Ori, Dori, Fili, Kili, Oin, Gloin, Bombur, Bofur, Bifur, Balin and Dwalin. I gave Thorin his own post which you can view here.
Nori, Ori and Dori were brothers, and were from a group of dwarves called Durin's Folk. All three brothers played the flute, and were remote kinsmen of Thorin.
Ori can also be found in the Stargate franchise as the name of god-like aliens that have ascended to another plane of existence.
Fili and Kili were also brothers, and were the youngest of the dwarves. Thorin was their uncle. They were often used as scouts.
Oin and Gloin were brothers and were cousins of Balin and Dwalin. Gloin was the father of Gimli, the dwarf that belonged to the Fellowship of the Ring in the Lord of the Rings.
Bombur and Bofur were brothers, and Bifur was their cousin. Bombur was known for being fat and late for everything. Bofur and Bifur both played the clarinet.
Balin and Dwalin were brothers. They both played the fiddle.
Although they seem less useable than other Tolkien names, some of the dwarves names have seen some limited use in 2011. The name Balin was given to 40 boys in 2011. Kili was given to 6 girls, this usage is probably not related to The Hobbit. It's probably more likely a variation of Kiley. Nori was given to 18 girls. I also doubt this is related to the Hobbit. Nori is also a boy's name in Japanese that means 'rule, or ceremony'. Ori was given to 53 boys, but it is also a Hebrew name that means 'my light'. Dori was given to 13 girls, most likely as a variation of Dora. Although Dori is a also a male Hebrew name meaning 'my generation'.