In his victory speech, De Blasio, who ran on a tax-the-rich platform that contrasted sharply with Bloomberg's record, declared that New Yorkers "have chosen a progressive path" and were united in the belief that "our city shall leave no New Yorker behind."
In Washington state, voters were deciding whether to require the labeling of genetically modified food. And in Colorado, they approved a measure to tax marijuana at 25 percent and dedicate the proceeds to regulating the newly legalized drug and building schools.
Turnout was relatively light given that it was not a presidential or congressional election year, and voters were primarily hard-core partisans.
In New Jersey, with 99 percent of precincts reporting, Christie had 60 percent of the vote to 38 percent for Democrat Barbara Buono, a state senator. He is the first Republican in a quarter-century to receive more than 50 percent of the vote in New Jersey, a state that voted overwhelmingly for President Barack Obama last year.
"Thank you, New Jersey, for making me the luckiest guy in the world," Christie said in a victory speech in the shore town of Asbury Park.
Christie drew on support from Democrats, independents and minorities in his win. That could position him to argue that his emphasis on pragmatism over ideology makes him the most electable Republican in what could be a crowded 2016 presidential primary field.
But it's not clear if Republican primary voters, who tend to be more conservative and ideological than the general electorate, will warm to the brash governor of a northeastern state. Republicans were fuming when, in the final days of last year's presidential campaign, Christie lavished praise on Obama for his response to a devastating storm that struck New Jersey.
In Virginia, McAuliffe, a former top Democratic Party official and close friend of Bill and Hillary Clinton, defeated Cuccinelli, the state attorney general. With 99 percent of precincts reporting, McAuliffe had 48 percent of the vote to 45 percent for Cuccinelli, with Libertarian Robert Sarvis receiving 7 percent.
"Over the next four years most Democrats and Republicans want to make Virginia a model of pragmatic leadership," McAuliffe said in his victory speech. "This is only possible if Virginia is the model for bipartisan cooperation."
Cuccinelli's candidacy was hurt by his ties to the small-government tea party movement, which is widely blamed for instigating last month's federal government shutdown. A large number of federal employees live in northern Virginia, where McAuliffe received large majorities that finally put him over the top.
Preliminary results of an exit poll conducted for The Associated Press and the television networks found that about a third of Virginia voters said they were personally impacted by the shutdown, and nearly half said Republicans deserved the blame for it.
Cuccinelli also had to deal with a scandal involving the incumbent Republican governor, Bob McDonnell, who was barred by law from seeking re-election; a strong campaign by the candidate for the Libertarian Party, which favors a minimal role for government; and the tremendous fundraising prowess of his Democratic rival.
Cuccinelli had hoped to score points in the final weeks of the campaign by highlighting the bungled start to Obama's signature health care overhaul. He emphasized that he was the first state attorney general to file a lawsuit to overturn the health law. McAuliffe had pledged to use the law to make more people eligible for Medicaid, the federal health program for the poor.
Among other races, former health care executive Mike Duggan was elected mayor of Detroit, now undergoing the largest municipal bankruptcy in U.S. history. In Boston, Martin Walsh, a Democratic state representative, was elected to succeed Mayor Thomas Menino, who wasn't seeking re-election after more than two decades in office.
