Mr Obama made his birth certificate public last July
During the 2008 US presidential election, rumours began to circulate on the internet that Barack Obama had not been born in the United States, and was therefore not eligible for the presidency.
Mr Obama's campaign provided plenty of evidence to rebut the claims, including the candidate's birth certificate, but the chatter has not died down, and some people have even launched lawsuits to question Mr Obama's eligibility.
With Mr Obama now installed in the White House, the number of Americans who believe - despite all evidence to the contrary - that he is not eligible to be president, and that his birth certificate is a forgery appears to be growing.
And "birthers" - as those who doubt Mr Obama's eligibility for the presidency are pejoratively known - have started making their presence felt within the conservative movement.
What allegations are being made about Mr Obama?
The principal allegation is that Barack Obama was not born in the United States, and that he is therefore ineligible to be president, according to the US constitution, which states that "no person except a natural born citizen... shall be eligible to the office of President".
It is further alleged that any documents purporting to prove Mr Obama's eligibility are either insufficient or fraudulent.
Some of those challenging Mr Obama's eligibility allege that he was actually born in Kenya, or that he adopted Indonesian citizenship as an infant.
What documents have been presented proving Mr Obama's eligibility?
In June 2008, the Obama campaign - in an attempt to disprove another set of internet rumours that Mr Obama's middle name was Muhammad -
made public his birth certificate.
The document - a Certification of Live Birth - indicated that Mr Obama had been born at 7.24pm on 4 August 1961, in Honolulu, Hawaii.
Researchers have also dug up birth notices for Mr Obama printed in the Honolulu Advertiser and the Honolulu Star-Bulletin in 1961.
The newspapers received information about births from Hawaii's Department of Health.
Did the documents stop the rumours?
No. When Mr Obama's Certification of Live Birth was published, as a scanned document on the Obama campaign's website, some people began to question its authenticity.
It was alleged in blog posts, chain emails and internet forums that the document did not have an official stamp or seal and that it lacked an official signature. Some even suggested that the document had been faked using picture-altering software.
Was there any substance to these allegations?
No. Representatives from the Annenberg Public Policy Center's Political Fact Check project
examined the hard copy of the document
and verified that it did in fact bear an official seal, and had been signed by Hawaii state registrar Alvin T Onaka (using a signature stamp). Both the seal and the signature were on the (unscanned) reverse of the document.
Did that put the rumours to bed?
No. Although most people accepted the authenticity of the birth certificate, a new allegation emerged.
The document released by the Obama camp was a Certification of Live Birth, freshly created in 2007 by Hawaiian officials at the request of the Obama campaign, based on Hawaii's computerised records, not the original hand-written long-form "Certificate of Live Birth", created by the hospital at the time of Mr Obama's birth.
A Certificate of Live Birth contains more information, including the hospital name, and the name of the attending physician.
Campaigners alleged that Hawaiian law permits the issuance of Certifications of Live Births to people born abroad, and began calling on the Obama campaign to release the long-form Certificate of Live Birth, which they said would answer all of their questions.
WorldNetDaily, a website that has been at the forefront of the campaign to probe Mr Obama's presidential eligibility, has drawn up a petition calling on Mr Obama to release the document.
Has the Certificate of Live Birth been released?
It has not. But Dr Chiyome Fukino, Director of the Hawaii Department of Health, has released a statement confirming that she has "seen the original vital records maintained on file by the Hawaii State Department of Health verifying Barack Hussein Obama was born in Hawaii and is a natural-born American citizen".
And, as Janice Okubo, director of communications for the Hawaii Department of Health, explains, no-one who was born abroad could get a certificate saying they were born in Hawaii.
"If you were born in Bali, for example," Ms Okubo told the Washington Independent, "you could get a certificate from the state of Hawaii saying you were born in Bali. You could not get a certificate saying you were born in Honolulu. The state has to verify a fact like that for it to appear on the certificate."
Have campaigners attempted to air their concerns in the courts?
A number of lawsuits have been filed by people who question Mr Obama's eligibility, but all of them have been dismissed at the earliest stages.
In July, Stefan Cook, a major in the US Army Reserve who was due to be deployed to Afghanistan, filed a lawsuit seeking to block his deployment, on the grounds that his orders were invalid, because President Obama was ineligible to serve as commander-in-chief. His case was dismissed.
Have any mainstream politicians endorsed the campaigners' views?
Most Republicans have rejected the claims, but Alan Keyes, a former Republican presidential candidate, has filed a lawsuit questioning Mr Obama's eligibility, and Republican Senator James Inhofe has said he does not "discourage" the movement.