Something that's held up as "proof" that Obama had and used a foreign passport was his 1981 trip to Pakistan, during a time that US citizens were forbidden to travel into and out of that country.
And that would be quite questionable save for one little tiny problem.
There was no travel ban by either the US or Pakistan.
First we will go with the US State Department Travel Advisory for Pakistan for 1981.
(PDF here)
"August 17, 1981
Travel to Pakistan
Before traveling to Pakistan, American Citizens should be aware of the following updated visa requirements: 30 day visas are available at Pakistani airports for tourists only. As these visas are rarely extended beyond the 30 day time per visa. Tourists planning to stay longer should secure visas before coming to Pakistan. Any traveler coming into Pakistan overland from India must repeat must have a valid visa, as 30 day visas are not repeat not issued at the overland border crossing point at Wagha.
Any non-official American who is in Pakistan for more than 30 days must register with the Government's Foreigner Registration Office. Exit permits are required for those who have stayed longer than 30 days before they are allowed to leave the country. All Americans traveling to Pakistan on official business or private employment are required to have a visa before arrival, and as the Government of Pakistan's clearance process is often lengthy, we would urge those coming to apply at the nearest Pakistani Embassy or Consulate as far in advance of their scheduled arrival as possible
This supersedes requirements set forth in Department Publication M-264, "Visa Requirements of Foreign Governments."
Expiration Date: Indefinite"
Notice that line "Exit permits are required for those who have stayed longer than 30 days before they are allowed to leave the country." This can be normal for many countries with a contract worker base.
Some people will also cite the Exit from Pakistan (Control) Ordinance, No. 46, 1981 as proof of a travel ban within Pakistan. In short, this law:
"Authorizes the Government to prohibit, by order, any person or group of persons to leave Pakistan irrespective of the fact the the prospective traveller(s) has (have) proper travel documents. The Government may, on grounds of public interest, omit to specify the reasons for such an order. A review of an individual order to prohibit any person or group of persons to leave Pakistan is possible before the Government, but a decision after a review is final."
And in 2005 the Supreme Court of Pakistan further clarified the intent with this law as:
(PDF here)
"The Government of Pakistan has also notified Rules under this Ordinance called Prevention & Control of Human Trafficking Rules 2005, which provide guidelines for dealing with issues relating to support to the victim.
* Previous Laws (Foreigners Act 1946, Emigration Ordinance 1979, Passport Act 1974, Exit from Pakistan Control Ordinance 1981, PPC, etc) covered only human smuggling and related offences."
This law was enacted in Pakistan on 31 December 1981. In other words, the end of the year. And it looks like it was geared towards migrant workers and smugglers than the tourist trade. (Exit restrictions are common in many countries with a high guest-worker population, such as parts of the Middle East. When I worked in Qatar, I had in my passport an unlimited entry/exit visa, Otherwise I would have had to show a letter from my employer to be allowed to leave that country)
In addition, on 14 June 1981, The New York Times published a travel piece for Lahore, Pakistan, which said in part:
"Tourists can obtain a free, 30-day visa (necessary for Americans) at border crossings and airports. Transportation within Lahore is plentiful, with taxis, scooter rickshaws and horse-drawn tongas (especially in the old city) readily available. Insist that taxis and scooter rickshaws use their meters to determine fares, however. Fares for longer journeys (for example, to the Shalimar Gardens) may have to be negotiated; ask the hotel staff for help. (We paid about $2 by scooter for the round trip to Shalimar.) Tonga fares are always agreed on through bargaining; most rides should cost less than 50 cents."
However, on 23 August 1981, the United States Consul General for Lahore, Pakistan, one John S. Brims, added as an advisory:
"While tourists can obtain a free, 30-day, non-extendable visa to Pakistan at the Wagah border crossing (on the rail route from New Delhi to Lahore), tourists cannot make the reverse journey from Pakistan to India through the same crossing unless they already have an Indian visa. The Indians only offer this service, so far as I know, to tourists debarking at airports. We have had a number of Americans stranded in Lahore who did not know this, and they tend to be too discouraged to enjoy the city."
So we have several different sources that show that there was no travel ban to Pakistan (a US ally at the time) from either US or Pakistani sources. And therefore, no reason to believe there that Barack Obama would have used anything other than a US passport.
The Pakistani travel ban myth is busted.
