(CNN) - While Tuesday's elections haven't gotten nearly the attention that a candidate for next year's presidential election has, voters across the country were casting ballots on races that mattered to them locally and had implications nationally.
Even as Republican presidential candidate Herman Cain was holding a nationally televised news conference to rebut sexual harassment allegations from the 1990s, a measure in Ohio to overturn the anti-collective bargaining measure that Republican Gov. John Kasich signed into law earlier this year was being interpreted as a barometer of next year's presidential election.
Returns in Ohio were too early to make a call on that measure or another that would exempt Ohio residents from the compulsory health care mandate in the national health care measure passed last year.
CNN was able to project based on reported results that Democratic incumbent Gov. Steve Beshear will win a second term as Kentucky governor, easily beating Republican state Sen. David Williams. Beshear had about 60% of the vote and Williams had about 30%. Independent Gatewood Galbraith had 10%.
In another high-profile governor's race, it was too early to call a winner in Mississippi, where Republican Lt. Gov. Phil Bryant is considered the favorite over Hattiesburg Mayor Johnny DuPree, the Democratic nominee who would be the state's first black governor. Bryant is expected to succeed Republican Gov. Haley Barbour, a fellow Republican who is term-limited.
Mississippi voters also were casting ballots on a "personhood" amendment that would define "life" as beginning at the moment of conception and make all abortions illegal, including the termination of pregnancies caused by rape, incest or those that prove to be a grave threat to the life of the mother. While the initiative appeared to have lots of support, it was opposed by some National Right to Life groups, and the Catholic Church in Mississippi said the amendment is too extreme.
In another state race that has gotten national attention, the chief architect of Arizona's controversial immigration law, state Sen. Russell Peace, faces a recall election.
In Virginia, Republicans were trying to win control of the state Senate. If they succeed, they would control both the state Senate and House, and the top three statewide positions - governor, lieutenant governor and attorney general - in an important swing state.
In another much-watched battleground state, a special election in Iowa will decide which party controls the state Senate.
Maine and Mississippi were the arenas for fights over voters' rights and could serve as a gauge for similar referendums next year.
Question 1 in Maine would repeal the same-day registration law that was passed earlier this year. Mississippi's Initiative 27 would make photo IDs mandatory at polling places. If passed, Mississippi would become the 15th state to require photo IDs to vote. Such laws have become popular with Republicans, who say that they are trying to reduce voter fraud. Democrats argued that Republicans are trying to suppress voter turnout, especially among people who tend to vote for Democrats.
Several major cities across the country were voting for mayors, with elections being held in Baltimore, Charlotte, Houston, Indianapolis, Philadelphia, Phoenix and San Francisco.
– CNN's John Helton and Robert Yoon contributed to this report.