From left, presidents George H.W. Bush, Barack Obama, George W. Bush, Bill Clinton and Jimmy Carter. (Nikki Kahn/ The Washington Post)

The Fact Checker is seeking reader suggestions for a video that will highlight the biggest presidential lies. We are looking for at least one false statement from each president — or authorized by a president — since the television age began.

Some are fairly easy to put on a list.

George H.W. Bush: “Read my lips: no new taxes”

Bill Clinton: “I did not have sexual relations with that woman”

Richard Nixon: “I’m not a crook”

Barack Obama: “If you like your plan, you can keep it”

But that’s like shooting fish in a barrel. What are the presidential lies that are less known — and potentially as significant? Should we consider whether a president asserts he did not mean to mislead, that he was misled himself?

Many readers might want to add George W. Bush and statements about weapons of mass destruction in Iraq on this list. Bush has blamed faulty intelligence, though critics have charged the administration with cooking the intelligence in the first place.

There’s also Lyndon Johnson and the Gulf of Tonkin incident, and Ronald Reagan and Iran-Contra. Are there specific quotes we should highlight, such as “we did not trade arms for hostages.” In his mea culpa, Reagan said he firmly believed that to be the case when he said it, but conceded it turned out not to be true.

What about John F. Kennedy and the Bay of Pigs? In a letter to Soviet leader Nikita Khrushchev, one day after the CIA-backed invasion of Cuba had started, he said, “I have previously stated, and I repeat now, that the United States intends no military intervention in Cuba.” Does lying to a foreign leader count?

Jimmy Carter famously said he would never lie to the American people. Did he live up to that pledge? Or should his toast to the Shah of Iran on Jan. 1, 1978 as “an island of stability in a turbulent corner of the world” be regarded as a lie or just simply naive? (The toast came after weeks of violent protests in Iran, and Mohammad Reza Shah Palavi was soon forced from power.)

Finally, there’s the case of Dwight Eisenhower and the U-2 incident. When an American U-2 spy plane was shot down over the Soviet Union in 1960, officials assumed the pilot had died and so concocted a false cover story (issued in the State Department’s name) that quickly collapsed after the Soviets revealed the pilot was still alive and had confessed. Eisenhower was forced to admit he had misled the American public.

Eisenhower later described it as his “greatest regret” as president. “The lie we told [about the U-2]. I didn’t realize how high a price we were going to pay for that lie,” he said. “And if I had to do it all over again, we would have kept our mouths shut.”

Of course, everyone hates to be caught in a lie. So what do you think? What should be on the list—and how should they rank?

Equally important, what do you emphatically believe should not be on the list?

Please put your ideas in the comment section below or use this form. You can also tweet suggestions to @GlennKesslerWP or go to our Facebook page

Update: We reached some conclusions and posted the video here. Thank you for the many good suggestions.