The Facts: This claim is dubious. The studies claiming these high numbers have been debunked. Better studies estimate the rate of false accusations as being in the single digits, generally in a range from 2-8%.
Here are some useful posts and papers on the subject. You'll notice they don't all agree with one another; It's a complicated subject.
False Rape Allegations Are Rare (YesMeansYes)
The reputable, methodologically sound reviews put the frequency of false reports in the single-digit percentages. There are people who, for propaganda reasons, keep saying that the incidence of false reports is much higher. They create these figures with biased reviews or intellectually dishonest mislabeling. ... A new study ... based on a review of every single rape allegation made to a US university police department — the study does not disclose which school — over a ten year period. The result: 5.9 percent false allegations.
Critique of Eugene Kanin’s Study Of False Rape Reports (Alas, a blog)
Eugene Kanin famously found that 41%, or perhaps 50%, of rapes reported to police are false. Kanin's study is both badly designed and unverifiable; more reliable studies have found that between 2% and 8% of rapes reported to police are false reports.Here's the Kanin study being discussed. (pdf).
False Allegations Of Rape Not Common – Or Are They? (Alas, a blog)
More on Kanin.
Report on False Reporting Of Non-Stranger Rapes (abyss2hope)
A discussion of a paper that notes:
In the research literature, estimates for the percentage of sexual assault reports that are false have varied widely, virtually across the entire possible spectrum. For example, a very comprehensive review article documented estimates from 1.5% to 90% (Rumney, 2006). However, very few of these estimates are based on research that could be considered credible. Most are reported without the kind of information that would be needed to evaluate their reliability and validity. A few are little more than published opinions, based either on personal experience or a non-systematic review (e.g. of police files, interviews with police investigators, or other information with unknown reliability and validity).The paper reviews recent research and notes that the most credible studies find "the rate of false reporting for sexual assault is in the range of 2-8%."
NOTE: the link to the study on abyss2hope is broken. This one works. (It's a pdf.)
Why it's so hard to quantify false rape charges, by Emily Bazelon and Rachael Larimore (Slate)
[I]sn't the rate of false rape charges an empirical question, with a specific answer that isn't vulnerable to ideological twisting? Yes and no. There has been a burst of research on this subject. Some of it is careful, but much of it is questionable. While most of the good studies converge at a rate of about 8 percent to 10 percent for false rape charges, the literature isn't quite definitive enough to stamp out the far higher estimates.
Anti-feminist myths debunked (Pandagon)
Contains an interesting discussion of the Kanin study.
Claims about McDowell's research into false rape allegations are not credible (Feminist Critics)
Discussion of another study that found a high percentage of false accusations.
Why Women Allegedly Lie About Rape (abyss2hope)
Also discusses McDowell's Air Force study
The myth of women’s false accusations of domestic violence and rape and misuse of protection orders (Michael Flood)
Myth: Women routinely make up allegations of domestic violence and rape, including to gain advantage in family law cases. And women use protection orders to remove men from their homes or deny contact with children.
Facts: The risk of domestic violence increases at the time of separation. Most allegations of domestic violence in the context of family law proceedings are made in good faith and with support and evidence for their claims. Rates of false accusations of rape are very low. Women living with domestic violence often do not take out protection orders and do so only as a last resort. Protection orders provide an effective means of reducing women’s vulnerability to violence.Note: I think this paper lowballs the estimate of false rape accusations. See the YesMeansYes article above for what I think is a more reasonable take.
False Allegations, Recantations, and Unfounding in the Context of Sexual Assault, Oregon Attorney General’s Sexual Assault Task Force (pdf)
Explains why recantations cannot be taken as definitive proof that an allegation is false.
Because recantation is used so frequently by victims to halt criminal justice involvement, it should never be seen, in and of itself, as indicative of a false report.
Another kind of false allegation:
The myth of false accusations of child abuse (Michael Flood)
Myth: Women routinely make false accusations of child abuse or domestic violence to gain advantage in family law proceedings and to arbitrarily deny their ex-partners’ access to the children.
Facts: Allegations of child abuse are rare. False allegations are rare; False allegations are made by fathers and mothers at equal rates; The child abuse often takes place in families where there is also domestic violence; Allegations of child abuse rarely result in the denial of parental contact.(Note: Most data cited from Australia.)
Rape Myths Past and Present
An article in the British magazine New Statesman, by Joanna Bourke, Professor of History at Birkbeck and author of Rape: A History from the 1860s to the Present (Virago, 2007). Excerpt:
[W]hat is the risk of an accused man being falsely accused of rape? Popular prejudices estimate that around half of rape victims are lying, but a major Home Office research project in 2000-2003 concluded that only three per cent of rape allegations were false. Indeed, contrary to the notion that men are at risk of being falsely accused, it is much more common for actual rapists to get away with their actions. Around four-fifths of rapes are never reported to the police. And only five per cent of rapes reported to the police ever end in a conviction. This is the lowest attrition rate of any country in Europe, except for Ireland.
None of this is to say that people aren't falsely accused -- of rape, and of other crimes -- or falsely convicted. They are, and it's a tragedy. Here are two groups that advocate for the the falsely accused and falsely convicted:
The Innocence Project
The National Center for Reason and Justice
NOTE: I have added text and links to this post since I originally posted it.