Dry Bones is a skeleton version of Koopa. The way to "beat" them is to jump on their heads causing them to fall apart. But don't think that they stay in little pieces, beacause they will soon reassemble themselves to their original form! (as a skeleton that is!)
Dry Bones' first appearance is in Super Mario Bros. 3, but he can also be selected as an unlockable character in Mario Kart DS and Mario Party 7, and a starting character in [[ Mario Superstar Baseball.