Before Marco Rubio: A History of Florida Politicians Who Almost Were Vice Presidential Candidates

Senator Bob Graham: Walter Mondale, 1984, Michael Dukakis, 1988, Bill Clinton, 1992 and Al Gore, 2000.
Yes, Graham, perhaps Florida's most respected and talented politician of the recent past, was considered as a possible running mate for four straight Democratic candidates in a row.

Speculation of a Mondale-Graham ticket was mostly the media's doing, and Mondale wanted to make history with his selection. He ended picking Geraldine Ferraro, the first female on a major ticket.

Graham was actually thoroughly vetted by Dukakis in '88. The Dukakis campaign's major worry: Graham had made a cameo in a Jimmy Buffet music video. Seriously. They were pretty concerned about it, and ended up choosing Sen. Lloyd Bentsen.

Four years later Bill Clinton interviewed Graham for the job and Graham was a confirmed finalist, but Al Gore was chosen instead.

Graham was also briefly under consideration during the early stage of Gore's own VP search, but didn't make the short list.

"I humbly like to believe I could have gotten another 600 votes for him in Florida," Graham recently said.

Governor Reubin Askew: George McGovern, 1972.
Askew was reportedly asked by McGovern to be his running mate (as did lots of others, because, that campaign was a hot mess with little chance of winning), but turned the offer down. McGovern ended up settling for Tom Eagleton. It was revealed shortly after his pick that Eagleton had suffered from depression, and McGovern asked him to step aside and eventually chose Sargent Shriver.