But not that Clinton. I've heard a few people suggest him. First, he'd never do it. That would be a demotion. Second, Kerry would never let himself be overshadowed by someone of such mammoth proportions. Third, they're too much alike in terms of not having views and going with whatever's popular at the time. Kerry needs someone who looks principled. Fourth, I don't know if he wants to look like he's bringing back the Clinton years. As popular as he was, Clinton was also the most unpopular president up to his time, something Bush has now beaten him on (on both counts). So we know it would never happen.
Yet it's made me wonder if it could. Is it unconstitutional for a former president who served two full terms to run for vice-president? There's something in there about the vice-president having to be able to fill all the requirements for being president, so it couldn't be someone who (even if a natural-born citizen) was born in another country (though U.S. military bases and U.S. ambassadorial grounds count as U.S. soil even if they're within other countries). It couldn't be someone under 35 (at least I think that's the required age). Someone can be Speaker of the House or Secretary of State and be next in line for the presidency due to some deaths, resignations, or impeachment-convictions but then be unqualified to serve as president, but that's not true for a vice-president.
But those are the examples the line in the Constitution refers to. There's a later amendment that I believe says that someone may not run for president after serving at least 6 years as president. Clinton has done that, so he can't run for president. Does that mean he couldn't serve as president? Does it rule out his running for vice-president? Even if it rules out his running, could he be appointed vice-president? Could he then serve as president if the president died, resigned, or got impeached and convicted, or would he be passed over for the next in line (the Speaker of the House if qualified) as Henry Kissinger would have been (for the Secretary of the Treasury in his case)?