Balloon
For the balloon item held in the player's hand and given out by Phineas, see here.
Balloons, or balloon presents, sometimes float along in the air, but always carry a present along with them. In Animal Crossing, a player would have to hope that the present got stuck in a tree, meaning that it could be shaken down, but in Wild World, City Folk and New Leaf, presents could be shot down with a slingshot. If shot down over water, and it lands in the water the player will show the emotion shock and will be unable to retrieve that present.
Balloons seem to float randomly over the town, but they in fact originate on the edges of the map at specific times, different for each town. The times they will appear will all end with the same minute value; for example, if players see a present float in from the edge at 5:45, they can be sure that each time it floats in will be a time ending in the minute value "4" or "5" depending on the game. Presents can then appear at times such as 7:55, 2:34, or 3:15. They will not appear at times such as 6:22 or 2:17. In Animal Crossing: Wild World presents only appear from 10 a.m. to 4 p.m. In other games they appear 24 hours a day.
After the player shoots down 15 packages, a silver (Animal Crossing: New Leaf only, in Animal Crossing: City Folk silver slingshots are rarely found in Tom Nook's store) or golden slingshot will float across the town on either a golden balloon (Wild World) or a group of two silver / three golden balloons (City Folk and New Leaf). These balloons have to be shot down in order to obtain the silver or golden slingshot tools, which shoot two and three pellets respectively and differ in appearance to the store-bought varieties.
In Animal Crossing
Balloons generally appear randomly just above the player in Animal Crossing, and can sometimes float diagonally across town, unlike later games. There is no slingshot in this game, so the player would have to hope that the present got stuck in a tree, and then shake the tree to obtain it.
In Animal Crossing: Wild World
In Animal Crossing: Wild World, presents carried by balloons appear on the DS's top screen. They can now be shot sown with a slingshot, but only when the player is standing in the top few tiles of town.
Balloons only appear from 10 a.m. to 4 p.m., and only when the minute vale of the time ends with a "4". After 15 packages are shot down, the golden slingshot will appear, carried by a single golden balloon. If this is missed, it will reappear a couple of presents later. Rumors state that another 15 presents must be shot down, but these are false.
In Animal Crossing: City Folk
In Animal Crossing: City Folk, the balloon presents are the sole source for the Super Mario themed items, but common items can be shot down as well. Phineas the sea lion states that balloons actually come from the sky. This statement, however, cannot be proven.
Presents in Animal Crossing: City Folk return to appearing above the player, and take set routes at acre boundaries, which are the same routes that Gulliver's U.F.O. takes. The golden slingshot is carried by three golden balloons, and appears once the player has shot down a number of regular balloon presents.
In Animal Crossing: New Leaf
In New Leaf, presents can be caught by a net or shovel near the beach, once the balloon flies low enough. They are the sole source for balloon-themed furniture. They fly lower than in previous games and may fly to the south for a period of time if their path is obstructed by a building.
The silver and golden slingshots can be obtained once 16 presents have been shot down. The silver slingshot can be obtained more than once.