Heh...way back, the Vice-President was whoever was the runner-up in the general election. You can imagine how well THAT worked out.
"Damn, I lost the election to my political arch-rival, and now I can only be President if he dies.....MUHAHAHAHA".
The office of Vice President is kind of fascinating. In essence, you're the understudy for the Leader of the Free World. But constitutionally, it's a very ill-defined office. It's not explicitly part of the executive branch, although it is typically treated as such. And there was no clear indication as to whether the Vice President was supposed to become President on the death/incapacitation of the sitting President, or merely be an acting President until an election could be organized. Wasn't until John Tyler in 1841 that anyone had actually had to do it, and Tyler just jumped in with both feet and said, "Nope! I'm the President now. No need for a new election!". And that just became the pattern followed.
Wasn't even really until Roosevelt in 1940 that candidates chose their running mate. Prior to that, the party bosses did the choosing, typically to heal factional rifts in the party (For example, if this were still the method used, it'd probably have been Obama/Clinton in 2008 and something like Romney/Santorum in 2012). And Reagan was the first one to announce his choice of running mate BEFORE the convention.