Not necessarily the strangest, but the 1960 Kennedy/LBJ ticket was sort of a surprise. Kennedy wasn't seen as particularly liberal, and there usually would not have been much worry about the Dems carrying the "Solid South", but the fact that Kennedy was Catholic probably came into play here. Even though there was no love lost between the Kennedys and LBJ, Jack and Bobby apparently believed that Johnson on the ticket would make it more palatable for Southerners who might hesitate about voting for a Roman Catholic. There were stories that Kennedy just offered the VP to Johnson as a courtesy, expecting him to turn it down. I have never believed that, because Kennedy almost certainly would not have carried some Southern states he had to have to win. It is pretty much of a fact, though, that Bobby and LBJ despised each other. This was an example of ticket balancing, more of a regional than ideological variety, with the addition of a very popular figure in a state with a lot of electoral votes.
That, by the way, was a possible "stolen election". Kennedy won by a few more than 100,000 votes nationwide out of about 68 million total, and his margin of victory was very close in two key states, Illinois and Texas. The Daley Machine in Chicago, and Johnson's influence in Texas might have delivered the vote for Kennedy. Nixon publicly refused to challenge the result, ironically, he said, because it would instigate a Constitutional crisis. Privately, he had people pursue pushes for recounts in some states. (I always thought it was hilarious that the Dems sent one of Mayor Richard Daley's sons, Bill Daley, to Florida to see that everything was on the up and up in 2000.) Probably, though, Kennedy was the real winner. Nixon winning Illinois (which I think was obviously stolen by Daley; some Cook County precincts reported 120% voter turnout) would not have given him the victory. Kennedy's margin of victory in Texas was about 40,000 votes, and the alleged fraud, which could have very well been real, in the border counties would not have been enough to give Nixon the win.
In 1980 there was talk for a few days about a possible Reagan-Gerald Ford ticket. This sort of faded out. Reagan-Bush was an example of ideological ticket-balancing. Bush sort of balanced the very-conservative Reagan, and made the ticket more palatable to more liberal Republicans.
A couple of Vice-Presidential quotes: John Nance Garner, who served as VP under FDR from 33-41, said the Vice-Presidency was "not worth a bucket of warm (spit)" Of course he did not say spit, but, then as now, the other word wasn't considered appropriate in certain circles.
Supposedly, Teddy Roosevelt once told a story of a mother with two sons: one son went to sea, and the other became VP. According to TR, "neither son was ever heard from again."
After the 2004 election, I heard Dick Cheney say on TV, "I did my part again. I delivered Wyoming." Funny because Wyoming only has 3 electoral votes and had no effect on the outcome of the election.
Clinton Gingrich ??? Dan Quayle one of finest elected ???? Rove signing on with Hillarys camp ??? Yes I actually saw that one this morning As if it wasn't enough for your party to lose elections , Now they're losing their minds