There are few better examples of this than in Wyoming, one of the nation’s most consistent Republican Party strongholds.

There, Democrat Dave Freudenthal is midway through his second term as governor. It is a seat that Republican campaign planners had penciled in as a likely pickup in 2010, because the state’s term-limit law would forbid Freudenthal from again seeking re-election.

But a different scenario has developed over the past few weeks — the possibility of a lawsuit to overturn Freudenthal’s term limit.

In many other states, such a gambit would likely raise cries of “arrogance” and “abuse of power.” But few governors have enjoyed the kind of job approval ratings — with percentages in the 70s and 80s over the long term — that Freudenthal has. The conventional wisdom in Wyoming is that the incumbent would be a prohibitive favorite to win a third term should he persuade the state courts to let him run for it.

Wyoming aside, there are 16 states with elections to replace term-limited governors, and several will be heavily targeted for takeover by the opposition party.

Democratic strategists will almost surely be targeting open sets in states that typically have strong leanings to their party, such as Hawaii, where Republican Linda Lingle cannot run again; Rhode Island, where Donald L. Carcieri is in the same boat; and California, where movie star Arnold Schwarzenegger is winding down an often stormy two-term tenure.

Republicans will target three clearly open Democratic seats in states that voted McCain for president last year: Oklahoma, where Brad Henry is the outgoing governor; Tennessee, where Phil Bredesen is term-limited; and, at least for now, Kansas, where Kathleen Sebelius cannot run for a third term.

Kansas would lose its open-seat status if Sebelius becomes Obama’s secretary of Health and Human Services, a possibility that has been floated in recent weeks. Should that happen, Lt. Gov. Mark Parkinson, a Democrat, would become the interim incumbent governor.

Other Democratic open seats — in states that backed Obama but which have long histories of being competitive for both major parties — almost certainly will be top-tier Republican targets.

These include economically beleaguered Michigan, where Jennifer A. Granholm is reaching the end of her two-term run; Oregon, where Theodore R. Kulongoski is term-limited; Pennsylvania, where Edward G. Rendell is heading out; and Virginia, the only state in which the governor cannot run for re-election after one term.

Virginia Republicans this year plan a major bid to take over from outgoing incumbent Tim Kaine (who also is the new chairman of the Democratic National Committee). Bob McDonnell, who stepped down as state Attorney General to focus on his bid for governor, is virtually locked in for the Republican nomination, while the Democrats will have to wait until June to resolve a competitive three-way primary for their nomination.

This year’s other contest will likely be measured as a bellwether of both the Democrats’ recent upsurge in national politics and the ability of incumbents to weather the economic storm.

First-term Democrat Corzine enters his re-election campaign with tepid approval ratings, in part because some of his proposals to deal with persistent state budget problems that pre-date the recession have been unpopular. Christopher Christie, a former U.S. attorney who was heavily recruited by Republican officials, has entered the GOP primary, and one recent independent poll showed him with a small lead over Corzine.

But Corzine is bolstered by a long-running Democratic trend in a Northeastern state that has voted Democratic for president in every election since 1992; has favored the party in every U.S. Senate race since 1976; and has given the party two wins in a row for governor. And the incumbent, made wealthy by his past stint as a top Wall Street executive, has thrown tens of millions of dollars of his own money into his two previous successful statewide bids, for U.S. Senate in 2000 and for governor in 2005.