In Animal Crossing: Wild World, you would be able to obtain a slingshot for a price at Tom Nook's store. With the slingshot, you are able to shoot anything from the sky down, including balloons with presents and UFO's. The golden slingshot is obtained after shooting enough of the balloons down. The Golden slingshot will float into your town and you must shoot it down to get it. With it, you'll be able to shoot out three pellets at once. They returned in Animal Crossing: City FolkWii. There is a regular, and gold, but now there is silver, which shoots out two at one time. Now they are used to hit ballons that have presents on them, just hit the ballon with your slingshot, and the present will fall. This is the only way to get some Marioitems.
In Animal Crossing: New Leaf, the slingshot is similar to City Folk's with 3 tiers of slingshots. The slingshot is the only way to get the Balloon Set of items.