Please check out the following elections: 1876:2000 [harpweek.com] and 1796:2000 [wikipedia.org]. See also 1960:2000 [wikipedia.org]. If Nixon had demanded recounts in Texas and Illinois, that election may never have ended. If those recounts revealed the massive election fraud widely rumored in relation to Democratic Bosses Richard Dealy of Chicago and LBJ of Texas (the VP candidate), Nixon would have won in a sqeaker. Rumor had it that JFK may have been elected by a lot of dead people. Many Americans have forever been grateful to Nixon for going away quietly (at the time). Those are just the three elections that jump out of my memory right now. The Mess of 2000 was hardly the only messy, tight Presidential race in 224 years. Might as well revisit the 2000 election too: 2000:2000 [wikipedia.org]. Very impressive article on that most recent mess. It lists seven "close elections", including all of these I have listed and more.
BTW, another little-known fact is that Vice Presidents routinely try to succeed their President when his 8 years is up. Question: How many have succeeded lately? Answer: Martin Van Buren and George H.W. Bush. Their successful elections are separated by 152 years. Check out Van Buren's election. [wikipedia.org] Interestingly enough, both were ousted after only one term. No sitting VP has succeeded his President directly other than these two guys since 1836. Nixon doesn't count since it was 8 years after he had been VP before he was elected President.
Looks to me like people generally get tired of the same old faces in the White House after 8 years and throw the VP rascal out too. This was no doubt part of Gore's fate in 2000. Gore didn't help himself by appearing as a different characters in each of the three debates. I really thought that hurt him, especially in light of his existing reputation as a bit of an automaton.