Usually unlimited but its possible there is a limit for some cities.
Two
There are no term limits for mayor in Chicago, IL.
3 Consecutive Terms
A mayor is allowed to serve up to 2 terms. That's 4 years.
2 4-year terms
two-four year terms
A mayor's term for Alaska is three years. But I don't know how many terms they may serve.
I suppose it would depend on the city, but surely many cities do not have any term limits and mayors have been known to serve for many terms.
Ed Koch was the 105th Mayor of New York City, serving for 3 terms from 1978 to 1989. He had previously served in the U. S. House of Representatives.
Ed Koch was the last Mayor of The City of New York to have served three terms.
The Mayor of Tampa serves a term of four years. There are no term limits, allowing a mayor to serve multiple consecutive terms if re-elected. The mayoral elections are held in even-numbered years.
In Middletown, Connecticut, the term for a mayor is two years. The mayor is elected by the city's residents and can serve multiple terms if re-elected.