Rumpelstiltskin has a handful of powers: to spin straw into gold and to give said power to others; to make common objects fly; to, while angry, smash the ground with his right foot such that he sinks to his waist in it; to vanish at will 12 times a day; to make magically binding deals; and to turn children into diamonds. He is known for making many, many deals, and he always knows where the debts lie (his own and others'). As such, he is often desperate to collect so he can pay off another debt.
His name is merely a description: he uses stilts that rattle as he walks, making himself appear larger than he is.
Rumpelstiltskin often plays games where he makes others discover his Name, but he cannot help but sing songs about it when he thinks he is alone. It simply is beyond his nature to resist such foolery.
He has long worked for the Queen of Faerie as her treasurer, never quite able to pay off his old debts to her. Recently, he has fallen in with the Puck in the war against the Dealmaker, seeking to become a Broker if all goes according to plan.