The laws about term limits for governors in the United States vary from state to state. Each state determines its own system, and the rules can get a bit entangled and complex, at least in the view of outsiders. Before delving into the mysteries of term limits by state, it may help to know that, for the most part, a given term lasts four years, unless the official is impeached, except in New Hampshire and Vermont, where they serve for two years only. If a governor steps down or is removed from office, the lieutenant governor usually steps in.
Term limits are designed to keep the political system fresh, and to ensure that people do not have an opportunity to consolidate power. Governors can be tremendously influential in their states, making term limits rather critical, as one may easily become more like an emperor than an elected official if there are no limits on service. This is especially true in the case of large and powerful states such as New York, California, and Texas.
In Connecticut, Idaho, Illinois, Iowa, Massachusetts, Minnesota, New Hampshire, New York, North Dakota, Texas, Vermont, Washington, and Wisconsin, there are no term limits for this office. Officials can serve as many terms as citizens are willing to elect them. Virginia also lacks term limits, but politicians cannot serve consecutive terms, which prevents the formation of a dynastic gubernatorial office.
Alabama, Alaska, Arizona, California, Colorado, Florida, Georgia, Hawaii, Kansas, Kentucky, Louisiana, Maine, Maryland, Michigan, Mississippi, Missouri, Nevada, New Jersey, New Mexico, North Carolina, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, West Virginia, and Wyoming all limit governors to two consecutive terms. In many of these states, the person may run again after taking a hiatus, although it is a relatively rare event.
In Arkansas and Delaware, governors are limited to two terms, period, consecutive or not. Indiana, Nebraska, and Ohio allows them to serve as many terms as they like, but after two consecutive terms, they must take four years off. In Montana, one may serve eight years in every 16.
For those curious about term limits in American territories, Puerto Rico has no term limits, the Northern Marianas have an absolute two term limit, and those in the Virgin Islands must observe a four year waiting period after two consecutive terms, at which point they may run again. Guam and American Samoa limit their governors to two consecutive terms.