Woodrow Wilson’s most famous piece of political advice was “Never murder a man who’s committing suicide.” Rep. Anthony Weiner’s critics might keep that in mind. The Twitter disaster has undoubtedly ended his hopes of being New York City’s next mayor and may well cost him his seat in Congress.

But as a scandal it pales before Eliot Spitzer’s descent into political infamy when he was identified as being “Client No. 9” in an upscale prostitution ring. Within a week there were T-shirts for sale proclaiming “I’m Client No. 8!” and he was forced to resign as governor of New York. As he drove to make his resignation announcement, his car was tracked by helicopters through the streets of Manhattan like O.J. Simpson’s famous ride in a white SUV through Los Angeles.

Rep. Vito Fossella of Staten Island (is there something in New York’s water?) was arrested for drunk driving in Alexandria, Va., in 2008 and among the revelations that flowed from it was the fact that he had a 3-year-old daughter with a mistress. He declined to run for re-election. Then there’s former senator and vice presidential candidate John Edwards’s love child, the cover-up of which has now gotten him indicted. Whatever the outcome of the case, his hopes of being president are a distant memory.

It would seem that there has been an unusual number of such career-ending shenanigans of late, beginning with President Clinton’s affair with White House intern Monica Lewinsky that, somehow, he managed to survive politically. But hanky-panky in the political class is as old as the Republic.

Alexander Hamilton had a reputation not unlike Bill Clinton’s when it came to women. (Martha Washington even named one of Mount Vernon’s tomcats Hamilton.) In 1791, Hamilton, then secretary of the Treasury, began an affair with a woman named Maria Reynolds. When her cuckolded husband blackmailed him, Hamilton paid hush money to keep his wife from learning of the dalliance. But when James Reynolds was arrested for counterfeiting, he tried to swing a deal with the Jeffersonians, offering to expose corruption in the Federalist Party.

The Jeffersonians didn’t bite, because the scandal was personal, not official. It was evidently a more gentlemanly time in the late 18th century. But when rumors began to circulate after Hamilton’s retirement, Hamilton publicly confessed to the affair, in surprising detail. He never again held public office and lost much of his political influence.

Hamilton’s longtime political antagonist, Thomas Jefferson, was also subjected to rumor and innuendo about his sex life. Federalist papers published rumors about him consorting with one of his slaves, usually labeled “Dusky Sally” in the stories. Jefferson, a widower, never responded to the accusations and suffered no political damage from them. It would be 200 years before DNA evidence would make the reality of Jefferson’s relationship with Sally Hemings almost certain.

Probably the most famous sex scandal of the late 19th century involved Grover Cleveland when he was running for president in 1884. He was accused of having fathered a child with a woman named Maria Halpin, who had named the child Oscar Folsom Cleveland. Republicans began chanting, “Ma! Ma! Where’s my pa?” and Cleveland told his campaign managers to “tell the truth.”

He admitted to paying child support, but he may well not have been the father. Halpin, it seems, had been bestowing her favors on several men, including Cleveland’s law partner Oscar Folsom, and Cleveland took responsibility because he was the only bachelor among them.

When the Democrats won the election despite the scandal, they answered the chant of “Ma! Ma! Where’s my pa?” with “Gone to the White House. Ha! Ha! Ha!”

In 1940, Sumner Welles, undersecretary of state, joined FDR and a host of high government officials on a train to Alabama to the funeral of William Bankhead, who had been speaker of the House. On the way back to Washington, Welles got quite drunk and propositioned the porter for gay sex, offering money. The porter refused and told other porters.

The head of the Secret Service detail investigated enough to convince himself of the truth of the accusation. He ordered everyone to keep silent on the subject and, remarkably, for nearly three years the story was contained. But Washington has rumor mills second only to Wall Street’s, and the story began to leak, especially after Secretary of State Cordell Hull heard the tale. Hull, who had been born in a log cabin in the hills of eastern Tennessee, hated Welles, who came from the same Groton-Harvard-old-family background as FDR and had easier access to the president. Hull set another State Department official, William Bullitt, to investigate. Bullitt also hated Welles.

FDR heard that Bullitt was spreading stories—especially through Washington’s gossip-central of that era, Alice Roosevelt Longworth, Teddy Roosevelt’s daughter and Eleanor Roosevelt’s first cousin. When Bullitt tried to enter the Oval Office one day on routine business, FDR reportedly said, “Stand where you are. You’ve tried to destroy a fellow human being; get out of here and never come back.” But FDR knew that Welles had to go too. The details of the scandal did not come out for another 50 years.

Then there’s Wilbur Mills, chairman of the House Ways and Means Committee for 18 years, who in 1974 was arrested for drunk driving in D.C. That’s the least of it. His companion, a stripper named Fanne Foxe, known as “the Argentine firecracker,” tried to escape by jumping into the Tidal Basin. Mills was re-elected in 1974 but retired from office two years later after another seemingly drunk public incident.

And then there’s Oregon’s Bob Packwood, who resigned from the Senate in 1995 when it became clear that he would otherwise be expelled for serial sexual harassment of women.

And then there’s . . . But you get the picture. As the late historian Stephen Ambrose once explained on PBS’s “NewsHour” about the Clinton-Lewinsky scandal, “God created man with a penis and a brain and gave him only enough blood to run one at a time.”

Mr. Gordon is the author of “An Empire of Wealth: The Epic History of American Economic Power” (HarperCollins, 2004).