The Gallup organization has a poll out showing that both Obama and Clinton beat McCain in the 12 swing states that either Bush or Kerry carried by 5% or less in 2004. Ohio would be in this group.
This is from the article posted on the Gallup website:
PRINCETON, NJ -- Democratic front-runner Barack Obama has a four-point advantage over presumptive Republican nominee John McCain among registered voters residing in states that were competitive in the 2004 election. Obama has a comfortable lead in states John Kerry won comfortably in 2004, as does McCain in states George W. Bush won easily....
Hillary Clinton also leads McCain by the same 47% to 43% margin among purple-state voters. But she does not fare quite as well as Obama does in blue states, and she trails McCain by a slightly larger margin than Obama does in red states.
Besides Ohio, the article lists the other states that are what they call "purple" states. Here is Gallup's list:
Based on this definition, the purple states include New Hampshire, Pennsylvania, Ohio, Michigan, Wisconsin, Minnesota, Iowa, Florida, Colorado, Nevada, New Mexico, and Oregon.
In 2004 John Kerry carried Pennsylvania, Michigan, Wisconsin, Minnesota,Oregon and New Hampshire. George W. Bush carried Ohio, Florida, Iowa, Colorado, Nevada, and New Mexico. This means that they split the 12 states equally, but the six states that Bush carried out of the 12 had more electoral votes. Consequently Bush carried the electoral collge by a 286 to 251 margin. A candidate has to get at least 270 votes to win the electoral college, which has a total of 537 votes. (The reason why 270 is the magic number is that there is not a way to get just 268 electoral college votes, which would be a majority of the 537 available votes.)
Thus, the trick for either Democrat is to hold the states that Kerry carried and pick up another 19 electoral votes. Either Ohio or Florida would give the Democratic nominee enough electoral votes. Ohio has 20 and Florida has 27. The Democratic nominee could also reach 270 by carrying Colorado, New Mexico, and Nevada, which would give him or her exactly 270. Add Iowa to the mix and you would have another 7, which would give you a total of 26. If you took those four additional states, you would have won more electoral votes than you would have winning Ohio and only one less than than you would have by winning Florida. Under any scenerio, though, Ohio will be an important state in this year's presidential election.
UPDATE: Please note that there are 538 electoral votes and not 537. Please read comments for correct math.