Q105. "My local newspaper had an educational page about voting that showed all the things that had been decided by one vote. For example, it said that German was almost the official language of the U.S., losing by just one vote, and the Rutherford Hayes was elected President by just one vote. Are these things true?"
A. Hayes was, indeed, elected to the Presidency by just one vote ... but not by a single vote in the popular election. The U.S. uses a system called The Electoral College to technically choose the President. In 1876, Hayes got 185 votes in the Electoral College, and Samuel Tilden got 184. So, he did win by one vote.
The German language thing, however, is an urban legend, helped along, unfortunately, by popular newspaper columnist Ann Landers. The story, like so many myths, is based on truth, but has been twisted and stretched to today's "German but for one vote" story. It is unfortunate the newspaper used this example. In 1795, a vote in the Congress came up to decide whether to print the US Code in German as well as in English. During the debate, there was a motion to adjourn, which failed by one vote, but there is no record of the official vote on the final measure. The full story can be found here.
While researching this Answer, I found another page that refutes several other "one vote" stories, including that Oliver Cromwell was given control of England in 1645 by one vote and that Adolf Hitler was made leader of Germany's Nazi Party in 1923 by one vote. The page can be found at Snopes.com, a site with lots of other debunking of urban legends.
The fact that many of these stories are not true should not have any effect on your use of your suffrage right. The ability to vote is something people in other nations die for ... do not take it for granted.