The Boomerang is an item originally used by the Boomerang Bro. but, became used as a projectile by Mario & crew starting with Super Mario 3D Land after obtaining the Boomerang Flower power-up. It is also an item in the Super Smash Bros. series
Super Mario series
The Boomerang acts as one would expect a Boomerang would act mostly. When thrown by the Boomerang Bros., it travels in a straight line to a certain distance and then, returns to the Koopa, even if it moves. It doesn't hurt other enemies while out. When the player uses it, it acts similarly except it only hurts enemies and doesn't hurt any companion players.
In the Mario Kart series, it acts similarly to how it does in the normal Mario series. Obtained from a Boomerang Flower, the racer throw the Flower in front of them and returns the racer. Any other racers along the way also get hit. THe Boomerang bounces off objects like buses.
Super Smash Bros.
With Super Smash Bros. for Nintendo 3DS / Wii U, rather than using the Boomerang Flower, the game uses the boomerang itself as an item. it is a unique projectile in that it gets more powerful the more it is thrown increasing its damage and knockback with each throw.