The Boomerang is an item originally used by the Boomerang Bro. but it became used as a projectile by Mario and crew starting with Super Mario 3D Land which introduced the Boomerang Flower power-up. It is also an item in the Super Smash Bros. series.
The Boomerang acts as one would expect a Boomerang would. When thrown by the Boomerang Bros., it travels in a straight line to a certain distance and then, returns to the Boomerang Bro., 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.
A special blue Boomerang appears in some of the World-e levels in this game. It will kill most enemies it hits when thrown. It flies forward for a short while before it turns around, but does so only once, meaning that it must be caught mid-flight to be used again. Like the Goomba's Shoe, it will disappear when the level is completed.
Certain Boomerang Bros. also use these Boomerangs in the levels Slidin' the Slopes, Bowser's Last Stand and Bowser's Airship 2. If they are defeated while their Boomerang out, they will drop it for the player's use.
Super Mario 3D Land
This game introduces a new power-up called the Boomerang Flower, which gives Mario and Luigi the ability to throw Boomerangs at will. However, a new Boomerang cannot be thrown until the previous one has either returned or disappeared.
The Boomerang Flower returns and functions exactly the same as it did in 3D Land. The color of the Boomerang depends on which character throws it.
In the Mario Kart series, it acts similarly to how it does in the normal Mario series. Obtained from a Boomerang Flower, the racer throws the Boomerang in front of them and it returns to the racer. Any other racers along the way also get hit. The Boomerang bounces off objects like buses.
Super Smash Bros.
In 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.