From Nookipedia, the Animal Crossing wiki
The House is the player's central building. At the beginning of each game, the player purchases his or her new home from Tom Nook through a mortgage plan. Paying off the mortgage generally results in expansions to the house, though they differ from game to game.
The house can be furnished with hundreds of items. The carpet and wallpaper can be changed out, and even a custom pattern can be laid on the floor or the wall. Indeed, the house is expected to be well-furnished by the Happy Room Academy; players are encouraged to collect whole sets, series, and themes of furniture to net a higher score.
If a player does not play Animal Crossing for some time, he or she will return to find the house infested with cockroaches. They hide under furniture, and must be squished by the player to be gotten rid of. The cockroaches can be exposed by either moving or removing furniture.
Directly outside the front door is the mailbox, where the players can recieve mail from others.
 Parts of a house
Rooms: The normal rooms, where the player can place furniture where they want. The house gains more rooms as the player pays off his or her mortgage.
Attic: The highest room of the house that contains four beds, where all the players sleep to save the game, and a telephone, where players can change the game's options. Initially, it is the second floor, but after the third expansion, it becomes the third floor. It doesn't appear in the original Animal Crossing or in Animal Crossing: New Leaf.
 In Animal Crossing
The house first appeared in Animal Crossing as part of the Town Square. The Town Square includes four houses, so that four players can live in the same town on one memory card. The highest number of rooms you can have to place furniture in is three: a main big room, basement, and upstairs room.
This version of the house featured some notable exterior flourishes. Most important was the gyroid, the sentient object in front of the house. The gyroid was responsible for saving the game, meaning the player had to talk to it before they stopped playing. Also featured on this house was the ability to hang a pattern on the front door. Moreover, the completion of a museum collection of fish or insects yielded a weathervane or butterfly ornament, respectively. The mailbox was also present.
The lights inside were controlled independent of the furniture in Animal Crossing by pressing the 'Z' button, unlike in the following titles. Also, the storage space was dependent on the number of storage furniture units one had in the house. Each bureau, dresser, cabinet, etc. could hold three items.
The player can paint their roof by three methods: house expansion (excluding basement addition), buying paint cans from Nook, or helping Wisp.
The house in Animal Crossing expands as follows:
 In Animal Forest and Animal Forest e+
In Animal Forest, players will not be able to get a second floor or basement. After the player's house has been fully upgraded and fully paid off, the player will get a statue in front of the train station. The first one to do so will get a gold statue, the second will get silver, the third will get bronze, and the fourth will get jade. In Animal Forest e+, players will also get their own private island.
All players share a house, instead of having separate ones as was seen in Animal Crossing. The house also expands more than in previous games. The mailbox is shared by the players living in the house, but a player can only take out their own mail. The house is placed in a random location. Gyroids are now gone, which have been replaced with an attic. The attic can have four double-sized beds and will have a phone. Beds can be changed by the user. No other furniture can be placed in the attic and the floor and wallpaper cannot be changed.
A basement is no longer part of the expansion, as storage units can hold up to 90 items. Also, when the house owners fully expand and fully pay off their house, there is no reward, making house owners refuse to pay off their final mortgage.
After the player has completed all the expansions above, Tom Nook will give the option of the expansion choices below.
 Second floor expansions
 Left room expansions
 Right room expansions
 Back room expansions
 Basement expansions