In reading The Doomsday Machine, I encountered a number of striking facts about nuclear security that previously were unknown to me. I was particularly surprised by a list Ellsberg created of nuclear threats, i.e. the threat to initiate nuclear attacks if certain demands are not met. As Ellsberg argues, the idea that no nuclear weapons "haven't been used" since Nagasaki is a misrepresentation, their use has just evolved. He says:

"[Nuclear weapons] have been used in the precise way that a gun is used when you point it at someone's head in a direct confrontation, whether or not the trigger is pulled. For a certain type of gun owner, getting their way in such situations without having to pull the trigger is the best use of the gun...[and] all American presidents since Franklin Roosevelt have acted on that motive" (319).

What follows is a list^[1] of nuclear threats made by US presidents, their administrations, and other US military leadership, spanning direct threats to complex signaling, but all with the goal to intimidate some adversary^[2]. I've quoted directly or paraphrased from Ellsberg for all of what lies below, pulling those marked with a * from elsewhere in the text. I also added some links to the events they reference, for further context.

1. Hiroshima and Nagasaki [August 1945]: The were threats to drop more until the Japanese surrendered.
2. *The creation of the U.S. Strategic Air Command (SAC) [1946]: SAC was created for the function of delivering nuclear attacks on Russia when so directed, which Russians eventually became aware of.
3. Truman's deployment of B-29s [June 1948]: The B-29s were described as "atomic-capable" and sent to bases in Britain and Germany at the outset of the Berlin blockade. Considered critical by the administration to the Soviets choosing not to challenge the blockade in the air.
4. Truman's press conference on Korea [November 30, 1950]: He warned that atomic weapons were under active consideration (as they actually were) for Korea after China entered the war.
5. Eisenhower's secret threats to China [1953]: Eisenhower threatened China to force and maintain a settlement in Korea.
6. Secretary of State Dulles' offer to the French [1954]: He offered French foreign minister Bidault two (possible three) tactical nuclear weapons to relieve the French troops besieged by the Indochinese at Dien Bien Phu.
7. Eisenhower's defense of Quemoy against China [September 1954-April 1955]: There was an internal agreement between Eisenhower and Dulles that nuclear weapons were necessary as a last resort to defend offshore islands of Quemoy and Matsu, communicated to the Chinese by numerous statements and moves. Dulles thought this lead to the eventual negotiated resolution of the crisis.
8. Nixon's "diplomatic use of the bomb" [1956]: Used to deter Soviet unilateral action against the British and French in the Suez Crisis of 1956.
9. Eisenhower and the Lebanon crisis [1958]: Eisenhower's secret directive to the Joint Chiefs during the 1958 Lebanon crisis to prepare to use nuclear weapons if necessary to prevent an Iraqi move into the oil fields of Kuwait.
10. Eisenhower's continued defense of Quemoy [1958]: Eisenhower's secret directive to the Joint Chiefs to plan to use nuclear weapons against the Chinese if they attempted to invade Quemoy.
11. The 1958-1959 Berlin crisis.
12. The 1961-1962 Berlin crisis.
13. The Cuban Missile crisis [1962].
14. Numerous "shows of nuclear force" involving demonstrative deployments or alerts-deliberately visible to adversaries and intended as a "nuclear signal"-of forces with a designated role in U.S. plans for strategic nuclear war [?].
15. Johnson's defense of US troops in Vietnam [1968]: There was public discussion in the newspapers and in the Senate of (correct) reports that Johnson had been advised by the JCS of the possible necessity of nuclear weapons to defend Marines surrounded at Kha Sanh, Vietnam.
16. Nixon officials' defense of Chinese nuclear capabilities against the Soviets [1969-1970]
17. Nixon's threats to the North Vietnamese [1969-1972]: Nixon had Henry Kissinger secretly threaten  "massive escalation" against the North Vietnamese, which included the possible use of nuclear weapons.
18. Nixon's second defense of China vs the Soviets [1971]: Threats and a nuclear-capable naval deployment were made to deter (according to Nixon) a Soviet response to possible Chinese intervention against India in the 1971 Indo-Pakistani War. Alternatively, to deter India from further military pressure on Pakistan.
19. Nixon preventing Soviet intervention in the 1973 Arab-Israeli War [October 1973]: Nixon's NSC put SAC on high alert to deter the Soviets from intervening unilaterally with ground forces to separate the combatants in the Arab-Israeli war, by underscoring U.S. threats to oppose them by force and expressing U.S. willingness to risk escalation to all-out nuclear war.
20. Ford's response to the "tree-trimming incident" [August 19, 1976]: Ford placed nuclear weapons on DEFCON 3 alert in response to the "tree-trimming incident", a fatal skirmish in the demilitarized zone in Korea. In response, the U.S. commenced a show of force which threatened possible use of nuclear weapons, including flying B-52 bombers "from Guam ominously north up the Yellow Sea on a vector directly to...Pyongyang".
21. The Carter Doctrine on the Middle East [January 1980]: Although lacking any specific language, Carter's doctrine for the Middle East announced in his State of the Union address was surrounded by news sourced from authorized leaks, backgrounders, and official spokesmen all carrying the message that the president's commitment to use "any means necessary, including military force" against a further Soviet move into the Persian Gulf region was, at its heart, a threat of possible initiation of tactical nuclear warfare by the United States^[3].
22. Deterring a Soviet invasion of Iran [August 1980]: Serious consideration from both the White House and JCS of the possible imminent use of tactical nuclear weapons if a secret Soviet buildup on the Iranian border led to a Soviet invasion of Iran, followed by the expression of explicit, secret nuclear warnings to the Soviet Union. Presidential press secretary Jody Powell was quoted as describing it as "the most serious nuclear crisis since the Cuban missile crisis".
23. Regan's reaffirmation of The Carter Doctrine [January 1981]: His outgoing secretary of defense Harold Brown told interviewers, in words reiterated by Regan himself a month later, that we would keep Russia (which had invaded Afghanistan in late 1979) from moving into northern Iran or other parts of the Middle East in the 1980s under "the risk of World War III".
24. H.W. Bush's formal threats against Iraq during Desert Storm [January 1991]: The Bush administration threatened possible U.S. nuclear response to various possible "unconscionable actions" by Iraq in Operation Desert Storm.
25. Clinton's deterrence of North Korean nuclear development [1995]: Explicit, secret threats by the Clinton administration of nuclear use against North Korea on its nuclear reactor program^[4].
26. Secretary of Defense William Perry's threat against Libya [1996]: Public warning of a nuclear option by Clinton's secretary of defense William Perry against Libya's Tarhuna underground chemical weapons facility.
27. *U.S. contingency plans for Iran [2005-2006]: There were articles released which claimed that, on the directive of vice president Richard Cheney, there were U.S. contingency plans involving "large-scale assault on Iran employing both conventional and tactical nuclear weapons". President Bush described the article as "wild speculation", but seemed to betray that sense in a later interview^[5].
28. *US presidential candidates positions [2007]: Democrats Hillary Clinton, Barak Obama, and John Edwards and Republicans Rudolph Giuliani, Mitt Romney, Duncan Hunter, James Gilmore, and John McCain all echoed Bush's threat of "all options" being on the table. Obama had signaled it would be off the table for Afghanistan and Pakistan, but kept it on the table for Iran.
29. *Trump's responses to Christ Matthews [March 30, 2016]: He continued the language of keeping "all the cards" on the table^[6]. 

1. ^{^}

   This is partially covered by the Nuclear Blackmail and Brinkmanship lists on Wikipedia, which also include threats from other countries, but I couldn't quickly find it in full anywhere else. If there's interest, I can also collect the threats from other countries here as well. 

2. ^{^}

   The events mentioned cover everything from threats which were fulfilled (Hiroshima), to threats which were serious enough to generate a crisis (Cuban Missile Crisis), to threats that were probably bluffs (Truman's deployment of B-29s).

3. ^{^}

   Assistant secretary of state for public information William Dyess later made this clear in an interview:

   Q: In nuclear war are w committed not to make the first strike?

   Dyess: No sir.

   Q: We could conceivably make an offensive...

   Dyess: We make no comment on that whatsoever, but the Soviets know that this terrible weapon has been dropped on human beings twice in history and it was an American president who dropped it both times. Therefore, they have to take this into consideration in their calculus. 

^{^}

This followed the near-launce of an American convention attack in 1994. 

^{^}

Reporter: Sir, when you talk about Iran, and you talk about ow you have diplomatic efforts, you also say all options are on the table. Does that include the possibility of a nuclear first strike? Is that something that your administration will plan for?

Bush [emphatically]: All options are on the table.

^{^}

The interview:

Matthews: Can you tell the Middle East we're not using a nuclear weapon on anybody?

Trump: I would never say that. I would never take any of my cards off the table. 

Matthews: How about Europe? We won't use it in Europe?

Trump: I--I'm not going to take it off the table.

Matthews: You might use it in Europe?

Trump: No, I don't think so. But I'm not taking...

Matthews: Well, just say it. "I will never use a nuclear weapon in Europe."

Trump: I am not--I am not taking cards off the table.

Show all footnotes