The recounts that did work were in races with very small margins. Here are the three most famous.
1. The 2008 Minnesota Senate race
The stakes: Minnesota's razor-thin 2008 U.S. Senate race, which was the tipping point for Democrats' filibuster-proof supermajority in the Senate.
Initial result: On election night, Sen. Norm Coleman (R-Minn.) was ahead of challenger Al Franken (D) by just 206 votes out of more than 2.9 million cast, a slim enough margin to automatically trigger a recount.
Recount process: A months-long recount of all the state's votes put Franken ahead of Coleman by 312 votes. Franken declared victory and started hiring Senate staff. But Coleman challenged the recount's results in court, a challenge that went on for another six months and all the way to the state Supreme Court.
Finally, in June, the state Supreme Court upheld the original recount and declared Franken the winner. “The Supreme Court has spoken. I will respect its decision, and abide by its results,” Coleman said. Franken officially took the Senate seat seven months after the election.
2. The 2004 Washington state governor's race
The stakes: An open governor's mansion in Washington in 2004 and one of the closest governor's races in history.
The initial results: On election night, results showed Republican former state senator Dino Rossi leading Democratic Attorney General Christine Gregoire by 261 votes out of some 3 million ballots cast.
The recount: There were several different recounts, which found several different results. (“This election is a really good example of why different types of recount can matter,” Johnson said.)
First, a legally required electronic re-scan of ballots reduced Rossi's lead to just 42 votes.
Then the state Democratic Party requested a hand recount (Washington's first), which gave Gregoire a 10-vote lead. The hand recount uncovered hundreds of missing ballots, and the Democratic Party had to go to the state Supreme Court to get those votes counted, which gave Gregoire a 129-vote lead.
“This is the biggest display of democracy I have ever seen,” Gregoire said amid the recount.
3. The 1974 New Hampshire Senate race
The stakes: An open Senate seat in a swing state (New Hampshire, 1974) and what ended up being the longest contested election in U.S. Senate history, plus a unique appeal to the Senate itself to try to solve the race.
The initial results: On election night, GOP Rep. Lewis Wyman was leading Democrat John Durkin by 355 votes. Durkin and Democrats immediately demanded a recount.
The recount: It became a nearly year-long headache. The first recount declared Durkin the winner by 10 votes. This time it was Wyman's turn to demand a recount. (Sensing a trend here?) This next recount had Wyman ahead by two votes.
By this time, the outgoing GOP senator had resigned his seat, and the governor, also a Republican, appointed Wyman to fill his spot.
Durkin's last-ditch effort was to file a request to the U.S. Senate to have the chamber determine the results. His logic was that Congress is the final arbiter of its own elections — and how convenient for him, the Senate was Democratic-controlled.
This was the first (and so far only) time a Senate election was thrown to the Senate. And we can see why it hasn't happened since: The Senate spent some six months reviewing thousands of ballots and debating what to do. No surprise here: They couldn't decide on anything.
Eventually Durkin and Wyman ended up deciding that the race was just too close to call and agreeing to just start over and hold a new election(!). The special election was held in September, and Durkin beat Wyman by 27,000 votes.
But Durkin never was able to overcome the taint of that nasty election and was easily beaten in the next one. In 2008, he told the Associated Press he wouldn't have wished the experience on his worst enemy.