Side Somersault

The Side Somersault (referred to as Side-flip by Prima Game Guides) is a high jump which typically grants a small amount more height than the Backwards Somersault. It is useful when the player wants to immediately jump high to reach high ledges. To use it, the character must run in one direction, then simultaneously turn to run in the other direction and jump.

In Super Mario Sunshine, Mario only needs to face in one direction and turn around; therefore, Mario could execute a Side Somersault with almost no space to move.

Bowser uses it in Super Mario Galaxy as one of his moves in the second battle against Mario.

In Super Mario Galaxy 2, Yoshi can also Side Somersault.

Super Mario Sunshine
This jump comes in handy when trying to reach places a standard jump can't or for getting above large enemies.
 * Instruction booklet description:

In this case, face away from the wall and tilt to the left.

Immediately tilt back to the right and press .

Success!

Super Mario 3D Land

 * North American Website Bio: "This move lets Mario do a quick about-face and launch into the air with extra height."
 * European Website Bio: "While dashing, push the Circle Pad in the opposite direction and press the B Button (or the A Button) to perform a side somersault. Mario jumps higher than with an ordinary jump."