From Nookipedia, the Animal Crossing wiki
 In Animal Crossing
Each Animal Crossing town starts with six villagers. Over time, more move in until the maximum of 15 is reached. Once this occurs the game will cycle out the 15th villager every ten days or so while keeping the initial 14 villagers intact. A villager may mention moving in a random conversation and ask the player for an opinion, but the player's response does not affect villager movement. A moving villager will not pack up prior to leaving; their home will simply be removed from the map upon game load and a goodbye letter is sent to the player's mailbox. Unlike subsequent Animal Crossing titles, once a villager has moved out another usually replaces them immediately.
 Movement across memory cards
Players are able to travel to other Animal Crossing towns by speaking to Porter at the Train Station. Each time a player goes to visit another town, one of the traveling player's villagers is chosen at random to move out, and anytime a town is visited by another player, that town will receive the resident from the visiting player's town. This is the only way to cycle out one of the fourteen original villagers.
 Controlling villager movement
By taking advantage of the way villagers move across memory cards, the player can manipulate which villagers come and go. In order to do this, three memory cards are required: one with the primary town's Animal Crossing data, a second with space for travel data, and a third with a secondary town that will be used as a repository for unwanted villagers.
 Removing unwanted villagers
Because villagers are selected at random to move when visiting another town, moving out a specific villager is a matter of trial and error. To begin the process, follow these steps: (the town must have seven or more villagers in order for this to work)
This same process can be used in order to move in a desired villager from one town to another.
 In Animal Crossing: Wild World
In Animal Crossing: Wild World, villagers attempt to move by packing their furniture up in boxes. While the villager is packing, the player can convince him or her, although it may take several tries. If the villager is not convinced to stay, he or she will move away, leaving a signpost behind, together with the goodbye letter. Another villager will move in to replace that villager, usually of the same gender, within a week. Attempts to move occur every two days, and this causes villagers to forget their current hobby and switch to a different one if they are convinced to stay.
There are only three villagers present at the start of the game. The maximum is eight villagers.
 In Animal Crossing: City Folk
In Animal Crossing: City Folk, moving works similarly to Animal Crossing: Wild World, but rather than immediately packing their furniture in boxes, moving villagers will approach the player while outside and ask them whether they should move away or not. They can be convinced to stay as before, although it can again take multiple tries. If a week passes and the villager is not convinced to stay, they will pack their belongings. Once this happens, they cannot be convinced to stay; they will move out after two days and will send the player their departure letter.
As in Animal Crossing, there are six villagers present at the start of the game; one of each personality. One villager will move in each day for the next three days. The tenth villager can take up to a week to move in.
 In Animal Crossing: New Leaf
Moving in Animal Crossing: New Leaf works the same as in Animal Crossing: City Folk, but villagers will now tell the player the date that they will pack up their furniture. Another added feature is a plot of land that appears the day before a new villager moves in, which announces the villager's name.
Villager can move in anywhere (where there is space) in town in this game; signposts are no longer scattered around town. Furthermore, they might send the player their picture with their goodbye letter if the player has befriended them.
There are five villagers present at the beginning of the game, and they will never be smug or uchi villagers. Gradually, villagers will move in until there are nine of them in town. A tenth villager can also be obtained via the campsite, StreetPass or another town.