In answer to 81's question, "No," a Presidential debate has never won a single election.
Not. One. Time.
But the press myth about them is that they have. My suspicion is that this is little more than wanting to make things they cover of more importance than they are, but it's never happened.
A myth grew out of the 1960 JFK-Nixon debate - one that basically said Kennedy wiped the floor with Nixon and it put him on equal ground with the experienced Vice-President. That may or may not have been true, but that story is only about the FIRST debate. The rest of the debates are not even mentioned most of the time as though there was only one. In fact, there were FOUR, and JFK only "won" the first one - and only with the TV audience; those who heard the debate but didn't see Nixon sweating thought the VP won.
That myth is largely part of why there were no debates again for 16 years. And despite the myth around it, Ford didn't lose the election because of the remark about Poland, either. What he DID lose, however, was a week of time in a race he began 33 points behind and lost by 2 (and would have won with just a change of about 10,000 or so votes in two states).
As far as Reagan-Carter, well, YES....it's true that Reagan basically gained about one point per day from the day of the debate until the Election Day one week later. But how much of that was people getting up and hearing "today is the first anniversary of the hostages being captured in Iran"? The economy in 1980 was the worst I ever can recall as a child (and I lived through a bakery strike in England).
And do they matter in that sense? The only thing about a debate in the visual age for President is: a) you get to see both candidates on stage next to each other for probably the only time; b) you figure out which one you "like" better.
A lot of this is nothing more than two girls running for class office President and the purdier one (however defined) wins. It shouldn't be that - but unfortunately it is.