The tale was on the first compilation of tales by the Brothers Grimm, in the 1812 edition.

In order to make himself appear more important, a miller/commoner lied to the king that his daughter could spin straw into gold. The king called for the girl, shut her in a tower room with straw and a spinning wheel, and demanded that she spin the straw into gold by morning, for three nights, or be executed.
She had given up all hope, when a dwarf appeared in the room and spun straw into gold for her in return for her necklace; then again the following night for her ring. On the third night, when she had nothing with which to reward him, the strange creature spun straw into gold for a promise that the girl's first-born child would become his.

The king was so impressed that he let the miller's daughter marry his son, the prince, but when their first child was born, the dwarf returned to claim his payment: "Now give me what you promised". The queen was frightened and offered him all the wealth she had if she could keep the child. The dwarf refused but finally agreed to give up his claim to the child if the queen could guess his name in three days. At first she failed, but before the second night, her messenger overheard the dwarf hopping about his fire and singing.

"To-day do I bake, to-morrow I brew,
The day after that the queen's child comes in;
And oh! I am glad that nobody knew
That the name I am called is Rumpelstilskin!"

When the dwarf came to the queen on the third day and she revealed his name, Rumpelstiltskin lost his bargain. Rumpelstiltskin, in his rage, drove his right foot so far into the ground that he creates a chasm and falls into it, never to be seen again.
(text taken from Wikipedia)