From Sonic Retro
The Bounce Attack, also known as the Stomp, Bound Jump, and other names, was first introduced in Sonic Adventure 2, and also appears in Sonic Advance 2, Sonic the Hedgehog (2006 game), Sonic Unleashed, and other games. When Sonic presses the action button (usually or ) during a jump, he will crash down with great force before bouncing back up. In the 3D games, Bounce Attacks can often be strung together to reach high areas.
Unleashed has a bounce-free version of the move simply called the Stomp. After picking up the Stomping Shoes from Holoska, Sonic is able to press down the comically oversized switches to open doors. Using the Stomp move is also the only reliable way of killing Mole Cannons.
In Sonic Colours and Sonic Lost World, the Bounce Attack is a default ability. In various other games, players must find or purchase a "Level-Up" item to use the move; for example the Bounce Bracelet in Adventure 2.
In Sonic Adventure 2, by Spin Dashing toward a wall, jumping if necessary, and pressing so that Sonic bounces off the floor just before hitting the wall, he'll carry the bounce animation into the wall and translate the horizontal speed of the Spin Dash into vertical momentum off the wall. This is nicknamed the "Super Bounce", and it allows Sonic to reach exorbitant heights, up to seven times as high as a standard bounce can provide.