Of the seven you mention, only 2 were admitted into their first term by election. The others gained office via the natural death, assassination or resignation of the president.
I don't necessarily see what difference that makes. I was originally just pointing out that, recently, former Vice President's have accounted for a number of our former Presidents, and that it is a good place to position yourself to become president in the future, whether it be by assassination, resignation, impeachment, or running afterwards.
I don't think its that difficult for a VP to run for the presidency and even to win his party's nomination. However, looking at USA's history, it appears that often serving as VP creates stumbling blocks that makes it more difficult for the VP to win a first term in the presidency by election.
Yes, I agree with you to a point. A VP can have a certain stigma attached to it when running for the General Election. Namely that one can be seen as "riding the coattails" of the President with which they served (Hilary has experienced this, and she was only the First Lady of a President!), and to a lesser extent the impression of 'more of the same' in a finicky nation.
Some might argue that one of the reasons that Gore didn’t win the election was because he didn’t know how to handle Bill Clinton’s support or how to discuss his vice presidency in the Clinton administration given the fact that Clinton had almost been impeached and a sizable segment of the voters were unhappy with the Monica affair.
Gore lost for several reasons (and some still don't think he actually lost). Had he won his home state (TN), or if Nader wasn't on the ballot in FL (or if a few hundred of his supporters voted Gore in key counties), heck if
Pat Buchanon wasn't on the ballot in FL, he'd have won. Not to mention lackluster debate performances, a lack of clarity and charisma, and a few others as well.
Clinton still had a wide majority of support (IIRC around 60%) when he left office, I just think Gore failed to capitalize on it. But given all of this he still won the popular vote, and
nearly won the Presidency in one of the closest elections of all time (or is it? I forget).
IIRC, Bush won despite having to deal with a great deal of flack about how he called Reagan economics "voodoo economics” before he decided to accept the vice presidency in the Reagan administration. His Democratic opponent, Dukakis, was unusually inept in handling the PR aspect of his campaign and that probably had a great deal to do with Bush becoming the rare exception of a former VP getting voted into the Presidency.
Dukakis nailed up his own coffin, but Bush was another example (much like Gore, only Bush won), of a VP following his former popular running mate to the White House.
Despite the fact that Obama and Clinton have similar positions on many of the issues, because of the differences in their character I can't see how, hypothetically, Obama would have an easy time of it defending his role in a Clinton/Obama administration should he decide to accept the VP slot and run for the presidency, say in 2016.
(This is assuming that enough of the super delegates decide to ignore the popular vote and cast theirs for Clinton -- so far Obama is in the lead (and in the lead in donations as well) and has no reason to give up his campaign.)
My imagination doesn't extend that far to see what Clinton would do in a similar position. I'm still stymied trying to imagine sniper fire while accepting a card from a little girl at a relaxed welcoming ceremony at an airport in Bosnia.
I think it would be a wise political move to unite the Democratic ticket, mostly because I think it would knock McCain out of the race (and I'm a McCain supporter, OMG!

), and ensure a Democratic White House, and probably a Democratic Congress as well. Either way the ticket would be formed, the support would be much stronger than if either goes it alone, and would give the Dem Party free-reign to enumerate their agenda, as mandated by a landslide vote in Nov by the general public.
Hilary/Obama would be the conventional choice by some, for many of the reasons you posted. But I actually think an Obama/Clinton ticket would be equally good, because Hilary seems more to be a backroom-headbusting-dealmaker, while Obama is better in speeches and public appearances (and really one of the most charismatic political figures on the scene in a while).
Another issue is that at this point its difficult to see how either candidate would be willing to give the other one any meaningful responsibilities as VP, and IMHO the loser would be better staying in the Senate where they would have much more control over their political career.
Both Senators come from Democratic states (NY & IL), so I don't think the Party has to worry too much about losing seats.
Deciding to accept the VP on the off chance that the president might pass away, be murdered or forced to resign while perhaps statistically viable (about 1 out of 5 chances (5 out of roughly 25 terms in the past 100 years)), just seem too morbid to contemplate.
Not just that, but the credentials being a VP in a successful administration can give one the opportunity to run for President him/herself.