Republican Chris Christie, who already is being touted as a possible presidential candidate, has been reelected governor of the northeastern U.S. state of New Jersey.
Votes are still being counted. But exit polls give Christie a wide lead over his Democratic opponent, State Senator Barbara Buono.
The popular Christie became a national figure when Superstorm Sandy devastated his state last year. He pleased liberals but angered conservatives when he became friendly with President Barack Obama in working to clean up storm damage.
In the nation's other closely watched election, exit polls say the governor's race in Virginia is too close to call. Democrat and close friend of former president Bill Clinton, Terry McAuliffe, is running against Tea Party conservative Ken Cuccinelli.
Voters in several major cities, including Atlanta, Boston, Detroit, Houston and Miami, are electing mayors. New York City may get its first Democratic mayor in more than 20 years. Polls give Bill de Blasio a wide lead over Republican Joe Lhota. Three-term Mayor Michael Bloomberg, an independent, is barred from a fourth term.
U.S. political analysts are looking for clues from Tuesday's results to help predict the outcome of next year's congressional elections, when all 435 seats in the House of Representatives and one-third of the nation's 100 Senate seats are up for grabs.
Americans also are voting on a variety of ballot initiatives Tuesday.
In the western state of Colorado, which legalized recreational marijuana last year, voters will decide whether to impose a 25 percent tax on the drug. The money would go toward regulating the marijuana industry and building schools.
Voters in the state of Washington will decide whether to require genetically engineered food to be properly labeled.