Some conspiracy theories have much more traction than others, however.
For example, three times as many people believe U.S. regulators prevent people from getting natural cures as believe that a U.S. spy agency infected a large number of African Americans with the human immunodeficiency virus (HIV).
J. Eric Oliver, the study's lead author from University of Chicago, said people may believe in conspiracy theories because they're easier to understand than complex medical information.
"Science in general - medicine in particular - is complicated and cognitively challenging because you have to carry around a lot of uncertainty," Oliver said.
"To talk about epidemiology and probability theories is difficult to understand as opposed to 'if you put this substance in your body, it's going to be bad,'" he said.
For the new study, he and his colleague used data from 1,351 adults who answered an online survey between August and September 2013. The data were then weighted to represent the U.S. population.
The participants read six popular medical conspiracy theories and then indicated whether they had heard of them and whether they agreed or disagreed with them.
Like the theories about conspiracies to infect African Americans with HIV and to prevent citizens from accessing alternative medicines, the other theories on the list had mistrust of government and large organizations as themes.
They include the theory that the government knows cell phones cause cancer but does nothing about it, that genetically modified organisms are being used to shrink the world's population, that routine vaccinations cause autism and that water fluoridation is a way for companies to dump dangerous chemicals into the environment.
Some 49 percent of the survey participants agreed with at least one of the conspiracies.
In fact, in addition to the 37 percent of respondents who fully agreed that U.S. regulators are suppressing access to natural cures, less than a third were willing to say they actively disagreed with the theory.
With regard to the theory that childhood vaccines cause psychological disorders like autism and the government knows it, 69 percent had heard the idea, 20 percent agreed with it and 44 percent disagreed.
The only conspiracy theory with which more than half of the respondents disagreed was that a U.S. spy agency infected a large number of African Americans with HIV.
The survey results suggest people who believe in medical conspiracy theories may approach their own health differently, the researchers said.
For example, while 13 percent of people who did not believe in any conspiracies took herbal supplements, 35 percent of those who believed in three or more theories took supplements.
Overall, the researchers say people who believed in conspiracies were more likely to use alternative medicine and to avoid traditional medicine.
"Although it is common to disparage adherents of conspiracy theories as a delusional fringe of paranoid cranks, our data suggest that medical conspiracy theories are widely known, broadly endorsed, and highly predictive of many common health behaviors," the researchers write in JAMA Internal Medicine.
Oliver said the findings may have implications for doctors.
Instead of viewing patients who believe in conspiracy theories as crazy, he said doctors should realize those patients may be less likely to follow a prescription regimen.
"It's important to increase information about health and science to the public," he said. "I think scientific thinking is not a very intuitive way to see the world. For people who don't have a lot of education, it's relatively easy to reject the scientific way of thinking about things."