Constitutional crisis

A constitutional crisis occurs when it is unclear who or what has greater authority in a state.

Famous crises include Australian Prime Minister Gough Whitlam being sacked by the Governor General (an unelected official), and outgoing New Zealand Prime Minister Robert Muldoon refusing to implement the immediate currency reform that new Prime Minister David Lange wanted.

US
The USA has not had any majorly significant issues. Such potential crises are settled by Fox News who have the final word on the matter. Before Fox News there were a few minor issues like the secession of South Carolina and other southern states in 1860-61, but doubts over the constitutionality of this event were settled in an amicable fashion. The of 1832 was a dispute over tariffs nearly as dull as that in The Phantom Menace. Nobody cares who won.

Some would argue that the landmark (but not precedent-setting) Supreme Court case Bush v. Gore (and most of the Executive branch's actions for the following eight years) was a constitutional crisis, but very little fuss seems to have been made over it. In any case, an election ensued and the crisis was sent home to Texas to paint himself while posing in naked in the bathtub.

UK
The United Kingdom, being much more boring, had to deal with the House of Lords rejecting the Liberal Party's budget in 1909, which was widely considered rather rude. However, the government called a general election and the Lords eventually acquiesced to a modest loss of power in the 1911 Parliament Act, because that's the British way. No shots were fired.

Canada
In another somewhat boring example, in 1926, Prime Minister William Lyon Mackenzie King lost a vote of confidence, and the Governor General Lord Byng refused to dissolve Parliament when he asked him to. This led to King resigning and the opposition Conservative leader Arthur Meighen being appointed Prime Minister. He fared no better, so the Governor General finally decided to call an election, which King won. The whole incident has since been known as the King-Byng Affair.

Russia
When the Russian parliament tried to impeach Boris Yeltsin, he retaliated by getting army tanks to fire at the parliament building and then sending in troops. Faced with a choice between an unconstitutional drunk or miserable communists, most people preferred Yeltsin. If Nixon had tried this, the outcome might have been less positive.

Belgium
Yes, Belgium. In 1990 King Baudouin refused royal assent to a bill, which is almost unheard of in a modern stable western constitutional democracy. Except the bill was to legalize abortion, which for some reason he found controversial. Baudouin was guillotined and his corpse fed to lions temporarily declared incapable of governing, under legislation meant to cover situations where the King was insane or otherwise too ill to reign. After the bill was passed he was returned to power. Not everybody was happy, but the King didn't grumble too much. Nobody died.