Usually not important, unless the VP is a total bonehead.
Other (please clarify).
After all, Dick Cheney was a very active VP under GWB. Also, the VP is also the President of the Senate. Dick Cheney took advantage of that for procedural issues in the Senate despite times when the Democrats had a majority.
Also, we need to legalize recreational drugs and prostitution.
The VP is very important in my opinion, not because the VP has a lot of power, but because the choice of VP says a lot about the presidential candidate. The president chooses the VP as his(her) partner, his confidant, his friend, his successor. A poor choice of VP tells the public that a candidate makes poor decisions.
"It ain't what they call you, it's what you answer to." - W. C. Fields