Some 91 percent of respondents said they heard the much-disputed rumor that Obama was a Muslim and 22 percent believed it, the study found.
The survey found damaging rumors about Obama were more widely heard and believed than those about his Republican opponents John McCain and Sarah Palin, and people were far more likely to have heard, and believed, rumors about a candidate they opposed.
Some 59 percent of respondents had heard the rumor that Obama did not qualify to be president because he was not a natural-born citizen, although only ten percent of them believed it.
And 41 percent had heard that the bulk of donations to the Obama campaign came from "a handful of wealthy foreign financiers" and 20 percent of them believed it.
Meanwhile, some 40 percent of respondents had heard the false rumor that Palin banned books from the Wasilla, Alaska library while serving as mayor but only 13 percent of them believed it.
Just 11 percent had heard the false claim that Vietnam veteran McCain told 60 Minutes that he was a "war criminal" who "bombed innocent women and children" and only three percent believed it.
While frequent Internet users were more likely to have heard the rumors, they were no more likely than others to believe the rumors and were more likely to have heard challenges.
"When people looked for accurate information on the Internet, and they often did, they could find it," said study author Kelly Garrett of Ohio State University.
"Our results suggest that the Internet does not pose the kind of threat to public knowledge that some have imagined."
The randomized telephone survey of 600 people taken November 6 to 20 had a margin of error of 4.4 percent.