If you only get your politics through popular media, you may be forgiven for thinking that the Vice President's job is to be the foil for the President's public image. The first George Bush came across as a wise statesman while Dan Quayle decidedly did not.
Clinton was affable and charming, but Gore seemed stoic and almost wooden (he has loosened up considerably since leaving office, however). The second Bush was the guy next door while Cheney came across as Darth Vader, and gaffe-a-minute Biden is the perfect counter-agent to Obama's cool, collected facade.
This is no accident - part of choosing a running mate is to find someone who can connect with the portion of the electorate that the presidential candidate cannot. But the Vice President has other jobs, a few of which may surprise you.
This is his highest function and most important job, hands down. This is why it's so important for candidates to choose a running mate with "presidential qualities" - because s/he is literally a heartbeat away from the presidency.
Interestingly, his position as President of the Senate also has a bearing on his retirement, theoretically. The office of the Vice President does not come with a pension - his pension is given as a member of the Senate instead, and he must serve five years to be eligible. In other words, one-term VPs are out of luck. In reality, this doesn't matter much.
Retired Vice Presidents are so in demand as public speakers that they make an exceedingly comfortable living from speaking fees alone. They also write bestselling autobiographies, become lobbyists or consultants, or return to their pre-presidential career roots. They do just fine.
Constitutionally speaking, this is the limit of the Vice President's responsibility. Until relatively recently, many VPs complained about their limited role, feeling powerless to influence policy. Now, however, he functions in unofficial roles to influence policy through numerous means.
Oddly enough, the office of the Vice President is not assigned to any particular branch of government - he is assigned Executive duties by the President and Congress, but some argue that he could be seen as part of the Legislative branch due to his role as President of the Senate.
This split assignment gives him a highly versatile capacity to support the President's policies in a variety of ways - many of which are only now being discovered as modern VPs branch out from the potential reach of their predecessors.
Here's where the Vice President's "foil to the President" role comes in - the VP is frequently responsible for promoting the President's policies in the court of public opinion. If the President seems to be taking a softer, more moderate stance on an important issue, it's because the Vice President is out there taking a hard line.
While the President may catch plenty of flak for expressing strong opinions about unpopular positions and may hurt his chances of re-election, the Vice President is free to word things as strongly as he likes.
Here's a secret - most of Biden's "gaffes" aren't gaffes at all - they're carefully crafted masterpieces of speech-writing designed to get press attention and drum up the support of the people who would come to his defense. Brilliant.
The Vice President is also an honorary member of the National Security Council and sits on the Smithsonian Institute's Board of Regents - and unlike the President, has no term limits. Which is great, because when you look into the job further than you normally would it sounds like way more fun than being President.