How many votes seperated the winner from the loser?
There was once an election for a Montana state legislator where both candidates were tied. As in, the exact same number of votes. The winner was literally decided by the flip of a coin.
Personally, I think that Nevada’s method for resolving tied elections is much cooler. There, the candidates play a single hand of five card stud. It’s equivalent to a coin toss, but it has so much more style, don’t you think?
You may want to define this more rigorously.
There are huge numbers of elections decided by a single vote, and the smaller the number of people who vote the more likely this becomes. For that matter, in small elections ties are common and then some procedure must be devised for deciding a winner.
As I see on preview Chronos has already said.
sorry for the broad question: Close races on large levels… presidential, congress or state general assemblies. 
OK, then, let’s dip into the Fun Fact Pool o’ Weirdness!
And on a larger scale:
http://www.senate.gov/artandhistory/history/minute/Closest_election_in_Senate_history.htm
The race for governor of Minnesota in 1962 had a margin of 91 votes. 1.3 million votes were cast and the winner was the challenger, Karl Rolvaag (D), who’d unseated incumbent Elmer Andersen. Rolvaag didn’t get to assume office until mid-March of 1963 after four months of recounts and court battles. Four years later Rolvaag was defeated by Harold LeVander. Rolvaag was then appointed ambassador to Iceland by LBJ.
Some municipal elections here and there may have had very small (or nonexistent, i.e., dead tie) margins, but the US Presidential election of 2000 (Gore vs Bush) still trumps them:
a) An election involving hundreds of people that comes down to a margin of a tiny handful of people is less tight than an election involving hundreds of millions of people that still comes down to a margin of a tiny handful of people.
b) Viewed (simplistically) in terms of straight-up popular vote, you could make the case that the margin of victory was a negative margin. Less than zero.
c) Viewed (more accurately) as the sequence of “Chinese boxes” or “Russian dolls” that US Presidential elections actually are, the cascade of razor-thin margins involved as you unpack – electoral college, electoral college with Florida in contention, Florida, Florida a / Florida b / Florida c / etc. estimates / recounts and the extent to which they differ, and, finally (even though by this time it was administrative rather than a standard part of the actual vote) the decision margin on the Supreme Court bench – was astonishing. Every penny we pitched landed on edge at the exact same distance from the wall. We’ll not likely see another race so close in our lifetimes.
pre-emptive anti-hijack hijack: I have no political axe to grind in this thread. My opinion of our current President is available to anyone who wishes to do a search, but my opinion of the vote itself is that it was a statistical dead heat, a tie, not capable of being reconciled; the margin of error of our counting tools exceeded the margin of difference.
“Landslide Lyndon” Johnson won his first US Senate nomination in 1948 by a mere 87 votes.
For more than a month it was thought his opponent had won, then a ballot box was discovered. The discovered ballots went 202-1 for Johnson. Another surprise – the majority in that precinct had voted in the exact order as their names appeared on the county tax roll.
With regard to the US 2000 Presidential election, is it not true that even had Gore won Florida, there were enough states which might have gone to Bush on a recount to maintain the result?
Yes. The Gore states won Wisconsin(11) .22%, Iowa(7) .32%, NM(5) .06% and Oregon(7) .44%.
Bush got 271, needing 270 for a win. Had he lost Florida, then he needed to win Wisconsin, Iowa and Oregon. 271!
If he had lost Florida, won Wisconsin and NM and either Iowa or Oregon but not both, we have a TIE.