That is actually a tough question.
Spiro Agnew had to resign in disgrace and cut a plea deal in order to avoid criminal prosecution for accepting bribes as Governor of Maryland and as Vice President, so I think I’d have to go with him. He was actually pretty effective for a while as Nixon’s hatchet man, but resigning in order to avoid prison is a tough one to get over.
Still, there’s also Aaron Burr who, of course, was the incumbent Vice President when he killed Alexander Hamilton in a duel. I highly doubt that we’ll ever have a Vice President preside over the Senate despite being indicted for murder. Burr had also nearly screwed Jefferson over in the 1800 election and almost cost Jefferson the Presidency. Burr was supposedly Jefferson’s running mate, but when they tied in Electoral votes and the election was thrown into the House, Burr actively attempted to become President instead of Vice President (Who made sure that Burr didn’t become President? Alexander Hamilton.) That’s a pretty rough start to your President-Vice President relationship. Let’s not forget that Burr (replaced by George Clinton by this time) was charged with treason (he was acquitted) during Jefferson’s second term for conspiring to separate some of the recently-acquired Louisiana Purchase land from the United States in order to create a new nation. Shit, maybe Burr was worse than Agnew. Agnew never killed anybody (even if Alexander Hamilton was a bit of a dick).
Franklin Pierce’s Vice President, William Rufus DeVane King was so sick at the time of his election that he wasn’t even in the United States for the inauguration. He was attempting to recover in Cuba’s tropical climate and was actually sworn in as VP in Havana 20 days after Pierce took the oath of office. King never set foot in Washington as VP. He died 25 days after being sworn in.
Charles Gates Dawes was a very accomplished man — he won the Nobel Peace Prize for his work with helping Germany with its struggle to pay reparations for World War I. When he became Calvin Coolidge’s VP, Dawes stood up in the Senate and gave his own inaugural address — basically a 20-minute lecture insulting the Senators and the Senate’s rules. He pissed off everyone in the building, especially Calvin Coolidge, who was already pissed at Dawes for saying that he would not attend Cabinet meetings if Coolidge asked him to.
Ulysses S. Grant’s first Vice President Schuyler Colfax was knee-deep in the Crédit Mobilier and attempted to cover it up when it was being investigated while he was Vice President. He had a reputation for being a little shady. Abraham Lincoln once called him “A friendly rascal,” and continued to describe him as “a little intriguer — plausible, aspiring beyond his capacity, and not trustworthy.”
Daniel D. Tompkins was James Monroe’s Vice President for eight years, and most observers said that he was drunk the entire time. He presided over the Senate while visibly intoxicated, was often so drunk that he couldn’t perform simple parliamentary duties, and was described in terms such as “the most injured of men” (by Martin Van Buren) and “a degraded sot”. Three months after leaving the Vice Presidency, he drank himself to death.
Wow…we’ve had some shitty Vice Presidents. I could probably continue, but these ones were the worst.