Mythology and folklore
In Norse mythology, fairy tales, and sword and sorcery fiction and role-playing games, a dwarf is a sprite, a member of a humanoid race, much like humans, but generally living underground or in mountainous areas. Here they have heaped up countless treasures of gold, silver, and precious stones, and pass their time in fabricating costly armor. They are famed miners and smiths though, like humans, specialize in any number of trades. Generally shorter than humans, they are on average stockier and hairier, usually sporting a full beard. Dwarfish smiths created some of the greatest and most powerful items of power in Norse mythology, such as the chain which bound the Fenris wolf.
Dwarfs are also called little Hill-men (Swiss), Earth-men (Härdmandle, pl. Härdmändlene. - Swiss) and Kröpel (German). Dwarfs were described as the height of a 3-year old human child (about 3 feet tall), ugly and big-headed. Nidavellir is the land of the dwarves in Norse mythology. Some dwarfs of mythology and fairy tales are: Rumpelstiltskin, the dwarfs from Snow White and the 7 Dwarfs, Snorri, Dvalin, Lit, Fjalar and Galar, Alvis, Eitri, Brokk, Hreidmar, Fafnir, Otr, Regin, and Alberich (or Andvari).
As for non-Germanic cultures, the Egyptian gods Bes and Ptah were dwarfs. In Judaism, the wise men of the Talmud said that the Egyptian Pharaoh of the Bible and the Babylonian king Nebuchadnezzar were dwarfs.
"For then also in the country The good Dwarflings still kept house; Small in form, but highly gifted, And so kind and generous!" - The Fairy Mythology 
Other mythological beings characterized by shortness are:
The Dwarves' Cavern : (In Hasel, Germany) was once home to many dwarfs. This legend gives the cavern its name.
Harz mountains : (Germany) On the north and the south sides of the Harz mountains, and in areas of the Hohenstein region, there once lived many thousands of dwarves, according to local tradition. In the clefts of the cliffs still exists the dwarf caves.
Tyre : In ancient Jewish scriptures, dwarfs were numerous in the towers of the fortresses of Tyre.
Fairy tales with dwarfs in them
Aid & Punishment, Chamois-Hunter, Curiosity punished, Dwarf in search of Lodging, Dwarf-Husband, Dwarf's Banquet, Dwarfs borrowing Bread, Dwarf's Feast, Dwarfs on the Tree, Dwarfs stealing Corn, Dwarf-Sword Tirfing, Friendly Dwarfs, Gertrude and Rosy, The Hill-Man at the Dance, History of Dwarf Long Nose, Journey of Dwarfs over the Mountain, Laird O' Co', Loki & the Dwarf, Lost Bell, Nihancan & Dwarf's Arrow, Nutcracker Dwarf, Rejected Gift, Rose-Red and Snow-White, Rumpelstiltskin, Sir Thynnč, Smith Riechert, Snow White and the Seven Dwarfs, Thorston & the Dwarf, Wonderful Little Pouch, The Yellow Dwarf
Stories of dwarves may have a historical background: during the Bronze Age, tin miners from southern and southeastern Europe slowly migrated northwest, since the relatively rare tin, which is needed to make bronze, was more common in the north. Being southerners, they generally were of shorter stature than northern Europeans and had darker skin, hair and beards. Their knowledge of metallurgy might have seemed magical to the northerners, whose lifestyle was still neolithic; the southerners' superior weapons and armour might well have been perceived as enchanted. This would explain why stories of dwarves are especially common in Northern Europe, and also why dwarves are portrayed as workers, while few other mythological creatures seem to be associated with any kind of organized industry.
Traditionally, the plural of dwarf was "dwarfs", especially when referring to actual humans with dwarfism, but ever since J. R. R. Tolkien used dwarves in his fantasy epic The Lord of the Rings, the plural forms "dwarfs" and "dwarves" have been used interchangeably. (When discussing Tolkien's universe, though, only the latter should be used.) Two other plural forms, dwarrows and dwerrows, were also suggested by Tolkien, but he never used them in his writings, apart from the name 'Dwarrowdelf', the English name for Khazad-dűm or Moria, a calque of the Westron name Phurunargian.
The Dwarves were created by Aulë, one of the Valar, when he grew impatient waiting for the coming of Children of Ilúvatar. Ilúvatar gave them life after speaking to Aulë about what he had done and seeing that he was both humble and repentant.
Dwarves are long-lived, living at least four times the age of man, but are not prolific breeders, having children rarely and spaced far apart, and having few women among them. Dwarvish children are cherished by their parents, and are defended at all costs from their traditional enemies, such as giants, goblins, and orcs. A longstanding enmity between dwarves and elves is also a staple of the racial conception.
Dwarves in modern fantasy fiction
Dwarves are implacable foes, with terrific endurance, strength, and determination. They tend to use heavy armour, large axes, and rarely give up. In some tales, for example those of J. R. R. Tolkien, dwarves are also especially resistant to fire. Dwarves in the Dungeons & Dragons role-playing game are directly derived from Tolkien's dwarves, although many variants exist, such as the hairless, man-eating, desert-dwelling dwarves of the Dark Sun campaign setting. Like Tolkein's Dwarves, many other sources depict dwarves as holding magic, elves, and humanoid monsters in contempt.