This is quite a broad topic, so I will keep to the high style side of things. In general, plans grew larger and more complicate as time progressed. The changes generally occurred due to developments in function or technology. As another caveat, residential architecture in the United States varies greatly by region, and there are many regionally specific forms. The following is most applicable to English-speaking populations.

Moving beyond a simple one-room cabin, a common early form was the hall and parlor plan, which as its name suggests featured a large hall with an exterior door and a smaller parlor, allowing for the separation of a private space. The hall and parlor was carried over from England. This developed into the central-passage plan by the late 1600s, particularly in the tidewater area, which featured the same two linear rooms with a passage between them, where the exterior doors were placed. The passage could provide further ventilation in the humid climate from a cross breeze.

Early high style architecture, the Georgian (18th century), the Federal/Adamesque (c. 1780-1830), and the Greek Revival (c. 1820-1850) and the more middle-class single pile I-house form in the Midwest generally had simple (four-cornered) symmetrical linear or massed floor plans, just as their facades were symmetrical, e.g. Mount Vernon. The central passage was carried over, although sometimes altered to a side passage. Entertainment (front) and service (rear) rooms were on the first story, bedrooms and private space on the second. Especially in warmer climates, a summer kitchen separate from the main house might be used to keep the excess heat and odors from the kitchen away from the living space. Such homes might also have a "servants staircase" or a smaller rear stair allowing inconspicuous passage between floors.

The styles of the late 19th century, notably the Gothic Revival, Italianate, and Queen Anne typically had irregular floorplans. This supported the asymmetrical, rambling aesthetic. The additional complexity was made feasible by the railroads, which allowed access to varied, cheap, more or less ready-to-use materials through large portions of the country. Use of balloon framing allowed for more flexibility in design. Also, the rise of the cast iron stove (c. 1840) and the central furnace (c. 1880) for made heating more efficient and greatly reduced reliance on large fireplaces, and thus shaping rooms around them. Homes could therefore more easily have irregular or compound plans with more corners. Porches, often wrap-around porches, were an important part of the plans, allowing additional living space and serving a social function. The Queen Anne in particular saw the decline of the central passage/entry hall, sometimes described instead as the enlarging of the hall into an entertainment space/room itself.

That is in very general terms. Hopefully someone with more expertise can jump in on the twentieth century, where I have less knowledge.

Edit: added details and sources

Gelernter, Mark. A History of American Architecture: Buildings in their Cultural and Technological Context. Hanover: University Press of New England. 1999.

McAlester, Virginia and Lee. A Field Guide to American Houses. New York: Alfred A. Knopf, 2004.