In the Columbus suburb of Westerville, Romney got a vote from textbook editor Heather Froelich, a registered Republican who said she likes Romney's business background and believes he has the best chance to beat President Barack Obama in November.
"I know that he understands the economy," said Froelich, 40. "He has the right experience and values."
Republican Josh Brooks of Columbus said he had considered voting for Romney but Gingrich won him over with his energy plan for lowering gas prices.
"He's tough and he's got big ideas," the 32-year-old engineer said.
Besides presidential contenders, voters have plenty of choices to make. Those include an unusual match of two Democratic U.S. House members pushed together under congressional redistricting and a contested primary for the Republican nominee to oppose Democratic U.S. Sen. Sherrod Brown. There also are two judges competing on the Democratic side to challenge an Ohio Supreme Court justice and numerous candidates seeking legislative seats.
Matt Howells, 52, a contractor and Santorum supporter, voted at Albion Middle School in Strongsville, southwest of Cleveland. He wants a GOP nominee who understands how to get the economy moving at a faster pace and believes political gridlock in Washington means a change is needed.
Howells said he was frustrated with the GOP field, with Romney spending heavily, Santorum outspent and Gingrich "a has-been" with intellectual firepower.
"They really have an uphill battle," he said. "I really don't see a Republican winning the White House. I see it going down as Obama again."
Others voters weren't impressed with their options or how the Republican candidates had attacked one another.
"It's going to make me vote Democratic," said Chuck Horning, a 47-year-old accountant and one of the earliest voters at a polling site in the Cincinnati suburb of Anderson Township, a heavily Republican area.
He said he was so disappointed that he voted only on local issues, not in the presidential primary.
"I don't like the way the Republicans have gone after each other, and the Democrats aren't any better."
At the same site, self-described independent George Knoske, 48, said he has voted for Republicans in the past but backed Obama, a Democrat, on Tuesday. Knoske, who works in computer technology, said the 2012 GOP candidates "are not enough toward the middle for me."
Republican Nancy Beck Doak, a 52-year-old aquatics instructor voting in suburban Cincinnati, said she voted on a school issue but ignored the presidential race on the ballot.
"I don't care for any of them, Republicans or Democrats," she said.
The Ohio Secretary of State's office didn't forecast a turnout, but some polling sites had few people show up in the first hours of voting, though things appeared to pick up later in the morning.
Ohio Treasurer Josh Mandel has a well-funded effort to take Brown's seat back for Republicans after the Democrat's 2006 victory. But Mandel first has to overcome five other Republicans.
And northern Ohio Democrats must choose between veteran incumbents Marcy Kaptur and Dennis Kucinich, while four Democrats are vying for a new district that includes most of Columbus. The state's congressional map was redrawn because Ohio loses two House seats because of population changes reflected in the 2010 census.
Meanwhile, a Toledo-area plumber thrust into national politics during the 2008 presidential campaign is running for the Republican nomination for the northern Ohio 9th House seat. Samuel Wurzelbacher became known as "Joe the Plumber" for expressing working-man concern about taxes to then-candidate Obama.
There are 14 Democratic and 18 Republican primaries for House seats, and three Republican primaries for state Senate seats. Two experienced judges were in the Democratic primary to challenge incumbent Justice Robert Cupp this fall, and some 100 local school issues are on ballots across the state as districts grapple with funding issues.
Ohio voters are used to election attention in a big swing state that tests candidates with its geographic and economic diversity.
No Republican nominee has reached the White House without carrying Ohio. Obama carried the state in 2008, after it delivered George W. Bush's clinching re-election votes in 2004.
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Associated Press writers Lisa Cornwell in Cincinnati, Ann Sanner in Westerville, Kantele Franko in Columbus and Thomas J. Sheeran in Strongsville and North Royalton contributed to this report.
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