Both a flat stone and the "bouncing bomb" rely on Newton's Law of Action and Reaction, and the fact that water cannot be compressed. So, if a stone or bomb is travelling fast enough, and at a low angle, its collision with water will result in an opposite reaction which will send the object into the air, causing the "skip". the number of skips can be increased by hurling the object faster.
During the Second World War, a drum-shaped bomb — essentially a specially designed depth charge — spinning backwards at over 500 rpm, dropped at a sufficiently low altitude at the correct speed, would skip for a significant distance over the surface of the water in a series of bounces before reaching a dam. Its residual spin would run the bomb down the side of the dam to its underwater base. Using a hydrostatic fuse, an accurate drop could bypass the dam's defences and enable the bomb to explode against the dam.
For more information about stone skipping, see http://en.wikipedia.org/wiki/Stone_skipping
For more information about the bouncing bomb, see http://en.wikipedia.org/wiki/Operation_Chastise
