Answer:
Individual state constitutions allow for City charters to adopt a constitutional "home-rule" whereby, the citizens of a City may decide which form of municipal government they wish to implement. Some states, may however, impose certain restrictions. For example, a state may not allow a city with a population below 5,000 to perform any actor organize themselves in any fashion not expressly allowed by the state.
Hardly all-inclusive, there are primarily 3 forms of municipal government used in the United States. Anything else is some type of derivative of the basic 3 types. For example, in the state of New Jersey, 12 different types of municipal government are recognized. Illinois recognizes 5 basic forms of municipal government (six when you add incorporated towns), while Texas, only two.