Retrieving a lost item is a type of favor that a player may perform for a villager. This type of favor first appeared in Animal Crossing: City Folk where a villager would accidentally lose their key in the river. This was expanded upon in Animal Crossing: New Leaf with the introduction of a variety of lost items that can be found around town.
In City Folk
In Animal Crossing: City Folk, a key is an item that a villager uses to get into their house. From time to time, a villager will be seen walking only around the outside of their house and will state that they are locked outside and has lost the house key somewhere around town. The villager may further reveal the location, which is the river - including the waterfall and lake. The key can only be found after the player has talked to the villager.
The key appears as a small fish shadow in the river, about the same size as a crucian carp. Once the player has fished it out the river and returned it to the villager, the villager will give them a small reward, usually furniture, a Gyroid, or a small amount of Bells.
If the player fails to find the key, the villager acts normal the next day, suggesting that they eventually found a way into their house.
In New Leaf
In Animal Crossing: New Leaf, a lost item belonging to one of the villagers may randomly appear on the ground outside. The player can ask any villager if they lost an item. If the villager lose the item, then the player will be rewarded with a random fruit, clothing, or furniture. If the item does not belong to that villager, they will return it and wish the player luck. It appears in multiple different forms around the town, including a book, brown bag, and a mitten. If the item given is a fruit, it will not be a Perfect Fruit. Lost Items cannot be thrown away, sold, or dropped once picked up. There can only be one lost item in the town per day that may be returned to a villager.
If the item is not returned within a day, it will change in the villager's inventory to an item titled "What was this?" The only option will be to open it. This means that players can choose to keep the lost item and forgo increasing friendship with a villager. If the player sells the lost item to Reese, it will cost Bells to sell it.
Not delivering the item on time will lower the friendship between the player and villager, most likely the same amount as denying a request from a villager.
In New Horizons
In Animal Crossing: New Horizons, lost items function similarly to those from Animal Crossing: New Leaf. In addition to presenting the lost item to the villager, the player has the option to investigate the properties of the lost item beforehand to figure out the owner. If the player shows it to the wrong villager, they will be told the name of another villager who is searching for something they lost.