Andrew Gelman has a post up about Vice Presidents as punchlines, and tries to figure out why. The main thing that he omits from his speculation is that even Vice Presidents who were absolutely serious people were punchlines as Vice Presidents, as Tom Lehrer makes clear (from 1965: "I wonder how many people here tonight remember Hubert Humphrey? He used to be a Senator..."). Lyndon Johnson was no one's patsy, but he was just a punchline from January 1961 until Dallas. So while Andrew lists Biden as a punchline, and that's true as far as it goes, I don't think that Biden was a liability in the campaign or in office.
What I'm more interested in is the set of lists that goes like this:
List A: Eagleton, Shriver, Dole, Ferraro, Quayle, Lieberman, Palin
List B: Mondale, (George H.W.) Bush, Bentsen, Gore, Kemp, Edwards, Biden
List B are Vice Presidential nominees who had previously run for president, at least a little; List A are those nominees who had not run for president before their selection for the #2 spot (I think Cheney goes in List A, but it's a close call; he had at least flirted with running for president, and had far better qualifications for high office than anyone on List A).
I suppose a more serious study would be necessary, but just on quick inspection there sure seems to be an enormous gap between the two lists, no? I think everyone on List B was regarded as a decent pick; there certainly are no wash-outs. List A, on the other hand, is a disaster area. The contrast is even stronger if we recall that Edwards wasn't the joke in 2004 that he became in 2008, with (as far as we know so far) his affair still in the future, and if we recall that Dole was largely perceived as a disaster in 1976 -- the impressive portion of his Senate career was largely in the future at that point.
I wouldn't try to push the analysis earlier than the reforms of the presidential nomination process before 1972 and the onset of newer media norms between 1960 and 1980, but I will mention that Nixon and Agnew (List A) were a lot less successful as Veeps than were Johnson and Humphrey (List B). If anyone wants to do an empirical study, I'd suggest checking for the word "dump" with the various nominees. I think you would come up positive for most of List A, and negative for everyone on List B.
No question in my mind: if a presidential nominee asked me for advise about Vice, I'd tell him or her to make a short list limited to people who survived a presidential campaign with their reputations intact. Anything else is asking for trouble.