Presidential Elections took place in each of these years. What links them together? Why distinguish them from the other years, which also had presidential elections? Simple: When these elections took place, all in the modern television, term limit, and primary nomination era, the sitting president had been elected twice and couldn't run again. This is instructive history for the next contest, which could be historically unique, or fit to form.
In three of these cases, the sitting Vice President ran for the job. In all three, that person won the nomination handily. In all three cases, the incumbent president was relatively popular. Those would be 1960, 1988, and 2000. In only one case did the Vice President win, George H. W. Bush. Being a sitting Vice President is clearly no guarantee of victory when trying to win a third cycle for his party. Vice President Gore...well lets just not bring that up, because if we count him as the victor that changes the odds considerably. But he wasn't the victor, never took the office, that's reality.
In 2008, we see what we see in other general elections where the seat is open. The incumbent party loses after the eight year cycle. There are no examples of a candidate who was not the Vice President going on to win the general election for a third term in power. Yet.
Basically, it hard to win three cycles in a row for either party. But when it has been done, it was the sitting Vice President who did it. And even in those cases, losing was more common than winning.
If this is any kind of wisdom, it wouldn't be a bad bet to expect a Republican president next year. Especially considering if Joe Biden is not the Democratic nominee. Hillary Clinton, Bernie Sanders, Martin O'Malley, and probably Lincoln Chaffee all face daunting odds if history is any guide. They would be historic, unique victories if they won. Especially since the latter three are in no rush to ally themselves with incumbent president, all seeking to wrest the party from President Obama's grip. (A task that gives me quite a chuckle in its courage...or folly).
So, either 2016 will be a notable election if there is a Democrat in the White House in 2017, or it will be a fairly typical one to all our dismay.