From the Super Mario Wiki
Boomerangs are a type of weapon that have made numerous appearances throughout the Mario series. When thrown, a boomerang will fly forward, harming any foes who happen to be in its path, then circle back to the user. They are the weapon of choice of the Boomerang Bros., but can also be used by Mario and Luigi after they pick up the Boomerang Flower.
Super Mario Advance 4: Super Mario Bros. 3
A special blue Boomerang makes an appearance in some of the e-Reader levels of Super Mario Advance 4: Super Mario Bros. 3. When thrown, the blue Boomerang defeats most enemies it touches before returning to Mario, who much catch it using the B button if he hopes to re-use it. While a few Japan-only levels featured blue Boomerangs, only one of these was made available in other regions: the World-e level Slidin' the Slopes. Near the end is a Boomerang Bro with a blue Boomerang that is dropped when the enemy is defeated; the player can then pick it up and use it for the remainder of the level, though it disappears upon completion, much like a Goomba's Shoe.
There is also an e-Reader card released only in Japan that uploads a Boomerang to the player's inventory, allowing them to use a boomerang in any stage.
Super Smash Bros. for Nintendo 3DS / Wii U
Boomerangs appear as a new item in Super Smash Bros. for Nintendo 3DS / Wii U. They function like standard boomerangs in that they are thrown to attack opponents and return to the thrower, though for every time the player catches it the boomerang's attack becomes stronger. Other players can catch the boomerang after it is thrown, however.
Boomerangs have been used by Boomerang Bros. in all of their appearances to date. See the Boomerang Bro article for a more extensive list.
Super Smash Bros. for Nintendo 3DS / Wii U Trophy information