From Nookipedia, the Animal Crossing wiki
 In Animal Crossing and earlier
In early Animal Crossing games, villagers move out without warning, approximately every 10 days. Moving villagers leave with a goodbye letter in the player's mailbox. Moving boxes do not exist. Once a villager has moved out, another usually replaces him or her immediately, unlike later Animal Crossing games.
At the start of the game, there are six villagers present. Over time, more move in until the maximum of 15 is reached.
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, 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.
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.