Here's a horrible thought, can Bill run for VP? Clinton/Clinton ticket. The American people have a short memory span.
No he cannot. By the same amendment that bars a two-term president from serving again, such a person cannot serve as VP where they could be in a position to become the President again.
As Rummyfan pointed out in post #84, Bill Clinton cannot run for VP because he is ineligible to be elected President again. Besides that, electors cannot vote for two candidates from their own state, so if Bill and Hillary have the same legal address then the New York electors could not vote for both of them. (That's why Dick Cheney had to change his legal residence back to Wyoming in 2000, so that the Texas electors could vote for both Bush and himself.)