The study's lead author, University of Chicago sociologist Edward Laumann, called the findings stunning.
"I think it gives us a base for explaining why we had this enormous response to Viagra," he said.
The researchers said problems with sex are often coupled with other problems -- everything from emotional and health problems to lack of time, job pressures and money trouble. But they said they aren't sure which comes first, stress or problems with sex.
The study was published in Wednesday's Journal of the American Medical Association.
CBS News Medical Consultant Dr. Bernadine Healy said she was surprised at the level of dysfunction reported by women, particularly younger women.
"When we think of dysfunction in men, it is the older men who have health problems," said Healy. "For younger women, the explanation is different, and at the top of the list are problems with relationships."
The researchers based their findings on the 1992 National Health and Social Life Survey, a compilation of interviews with 1,749 women and 1,410 men.
The participants, ranging in age from 18 to 59, were asked if they had experienced sexual dysfunction over several months in the previous year. Sexual dysfunction was defined as a regular lack of interest in or pain during sex, or persistent problems achieving lubrication, an erection or orgasm.
Lack of interest in sex was the most common problem for women, with about a third saying they regularly didn't want sex. Twenty-six percent said they regularly didn't have orgasms and 23 percent said sex wasn't pleasurable.
About a third of men said they had persistent problems with climaxing too early, while 14 percent said they had no interest in sex. Eight percent said they consistently derived no pleasure from sex.
Overall, 43 percent of women and 31 percent of men said they had one or more persistent problems with sex.
The researchers had expected the overall numbers to be closer to about 20 percent for each sex.
Laumann said the findings could offer hope to millions, many of whom think they're the only ones having trouble in bed.
"Often they don't even admit it to their partners. It's the old 'I've got a headache' instead of 'I don't feel like having sex'," he said.
Dr. Domeena Renshaw, a Chicago-area sex therapist, said the results are not surprising, considering the long list of couples waiting to get into the sexual dysfunction clinic she has run at the Loyola University Medical Center since 1972.
In that time, she has treated nearly 140 couples who had never consummated their marriages, including a couple who had been wed for 23 years.
Study co-author Raymond Rosen, co-dirctor of the Center for Sexual and Marital Health at the Robert Wood Johnson Medical School in New Brunswick, N.J., said the survey provides much-needed information about women, who have often been excluded from studies about sexual performance.
He said the findings are the most reliable since Dr. Alfred Kinsey did his landmark studies 50 years ago.
Kinsey got similar results regarding impotence and failure to achieve orgasm but didn't ask about lack of sexual desire.
Too often, Rosen said, Americans have gotten their information about sex from magazines bought at the grocery-store checkout counter.
"As a scientist, it makes my hair stand on end," Rosen said. "It's terrible."