Every time there's elections coming up, people try to convince each other by saying "your vote could make the difference". So, I'd like to know if this has ever happened, or if it remains as just a possibility.
On which level do you mean?
Konrad Adenauer was elected German chancellor in 1949 by one vote of the Bundestag on September 15th 1949 (http://dipbt.bundestag.de/doc/btp/01/01001.pdf).
In Quebec in 1994 in the general election there was no difference in the votes between the first two candidates: http://www.quebecpolitique.com/elections-et-referendums/circonscriptions/elections-dans-saint-jean/#1994