Tinyhouses are currently facing a struggle against zoning bylaws. The exact reasons remain unclear, as their opponents give several reasons but in almost all cases, they are not supported by any evidence.
Whatever else it may be, this is a case of "exclusionary zoning".
Tinyhouses with wheels are usually considered by a municipality to be the same as a mobile home or travel trailer, though there are some considerable differences between them (post on tinyhousedesign blog about differences). Because tinyhouses have the potential to appeal to a wider audience than conventional trailers, advocates hold hope that they may be permitted more widely in the future. In the United States, some of the restrictions that lead to tinyhouses being banned have been ruled unconstitutional in some states. Some municipalities have minimum floor area requirements even for trailers.
Stationary tinyhouses, without wheels, but with a bathroom and kitchen, are considered a building and a dwelling, regardless of size, and usually the municipality or township requires that they be permitted before use as a dwelling. If there is no bathroom, it is usually not considered a dwelling, and does not require a permit if the floor area is under a certain size, e.g. 120 sq ft.
The City usually does not allow a permit, even if the minimum floor area is high enough. In some cases they appear to be permitted in some (e.g. rural) areas, for very restricted use e.g. the parents of the owner of the property can live in the house, if they occupy it continuously without an absence of more than 30 days, but no one else (see "standard garden suite agreement"). They may also require you to go through a zoning amendment procedure to get a zoning variance, to do something which was not specifically allowed in the zoning codes. Most municipalities ban everything except what is explicitly allowed, thereby inherently banning anything new/innovative/different/better, which the legislators would not have thought of.
However, for details in your area, you must check the local zoning bylaws, which are usually available on the web somewhere.
There are many examples of Tinyhouse_like_concepts, that are permitted in some cities, with or without a permit, such as the Vancouver laneway housing, Seattle cottage housing, and the Modpod or "Grannypod", which the state legislature of Virginia has ruled must be permitted, despite local municipal zoning that would ban them.
http://www.mapleridge.ca/assets/Default/Planning/pdfs/garden_suites_discussion_paper.pdf suggests accessory dwelling units may be permitted in some cities as by right.