The Ohio law, repealed by 61 percent to 39 percent, would have stripped the state's 350,000 public employees of most of their collective-bargaining rights and forced workers to pay at least 15 percent of their healthcare costs. The bill, known as Senate Bill 5, passed the legislature in March, and a similar bill passed in Wisconsin.
The Ohio bill was signed by Republican Gov. John Kasich. But opponents secured enough voter signatures to force a public vote before it could take effect.
At a news conference Tuesday night, Kasich congratulated the winners and said he would assess the situation before proposing any new legislation. "It's time to pause," he said. "It's clear that the people have spoken."
He said he would continue to work with local governments facing budget challenges, but warned there would be "no bailout" because "there's no money."
In Mississippi, voters rejected a state Constitution amendment that would have banned virtually all abortions and some forms of birth control by declaring a fertilized human egg a legal person.
The so-called personhood measure, known officially as Initiative 26, defined life as including "every human being from the moment of fertilization, cloning or the functional equivalent thereof."
In Arizona, the author of the state's tough and contentious immigration law -- the broadest and strictest anti-illegal immigration measure in the country -- conceded defeat in an unprecedented recall election.
State Sen. Russell Pearce, a Republican power broker and Tea Party movement hero, lost with about 45 percent of the vote to fellow Republican Jerry Lewis, who runs charter schools and garnered about 55 percent.
"If being recalled is the price for keeping one's promises, then so be it," Pearce said in his concession.
Pearce is the first state legislator in Arizona history to be removed from office through a recall election.
In Kentucky, Democratic incumbent Gov. Steve Beshear won re-election easily over Republican state Senate President David Williams. Kentucky is a culturally conservative state strapped with high unemployment that pundits said should have been ripe for a Republican win.
In Mississippi, Republican Phil Bryant topped Democrat Johnny DuPree to replace Gov. Haley Barbour, a Republican blocked from seeking re-election because of term limits.
In New Jersey, where the entire state legislature was up for grabs, Democrats held on to their majorities in both houses. Republican Gov. Chris Christie had set low expectations for his party, and both sides claimed the results as a victory.
Virginia state Republicans appeared poised to pick up a net two state Senate seats to reclaim the majority in that chamber and full control of both chambers and the governorship, ABC News reported early Wednesday.
The race hinged on an unknown number of provisional ballots in the 17th election district, where Republican challenger Bryce Reeves was leading Democratic incumbent Ed Houck by fewer than 90 votes. The remaining ballots were to be counted later Wednesday.
Across the country, most incumbent mayors in major cities running for re-election Tuesday won.
Philadelphia Democratic Mayor Michael Nutter won, as did Republican Indianapolis Mayor Greg Ballard and Baltimore Democratic Mayor Stephanie Rawlings-Blake.
Democrat Greg Stanton won in Phoenix, while San Francisco interim Mayor Edwin Lee appeared to have been elected that city's first Chinese-American mayor.
He was appointed interim mayor by the city's board of supervisors Jan. 11 to serve out the remainder of Mayor Gavin Newsom's term, after Newsom was elected California's lieutenant governor.