The CBS network's 60 Minutes programme, aired on Sunday, videotaped the Boeing 737 on a runway at Glasgow Airport in Scotland, saying it was able to trace it through a series of companies and executives that apparently exist only on paper.
It said the plane had made at least 600 flights to 40 countries, all after the September 11 attacks on the US, including 30 trips to Jordan, 19 to Afghanistan, 17 to Morocco, and 16 to Iraq.
The plane also went to Egypt, Libya and Guantanamo Bay, Cuba, according to the report.
The aircraft is part of the Central Intelligence Agency's "rendition" programme, in which suspects are sent to foreign governments for interrogation.
The agency has not formally acknowledged the programme's existence.
A German national, which CBS identified as al-Masri, told a reporter he was on vacation in Macedonia when he was arrested by police and held for three weeks, then taken to the airport, beaten by masked men, drugged and put on board the 737.
The plane left Skopje, Macedonia, and went to Baghdad and then Kabul, with al-Masri saying he awoke in a jail cell where his captors said: "You're in a country without laws and no one knows where you are."
Al-Masri told the network: "It was very clear to me that he meant I could stay in my cell for 20 years or be buried somewhere."
He added his fellow prisoners in the American-run jail were Saudi Arabians, Tanzanians, a Yemeni and a Pakistani who had lived in the US.
"It was very clear to me that [the interrogator] meant I could stay in my cell for 20 years or be buried somewhere"
Former US detainee
Al-Masri said he was in solitary confinement for five months before being released without an explanation.
According to the report, the jet also made 10 trips to Uzbekistan, where former British ambassador Craig Murray said the jet's nominal owner, Premier Executive Transport Services, kept a small staff at the airport in Tashkent.
Suffocation and rape
Murray said Uzbek interrogators use unusually cruel methods, including "techniques of drowning and suffocation, rape ... and also the insertion of limbs in boiling liquid".
He said he had complained to his superiors that information was being obtained by torture and sent his deputy to the CIA station chief to inquire about the practice.
"The CIA definitely knows," he told the television programme, adding that his deputy had confirmed that evidence "probably was obtained under torture but the CIA didn't see that as a problem".
He was ordered to return to London four months ago and has since left government service, CBS News pointed out.
The American authorities have yet to respond to the CBS programme's allegations.