Vice-President Biden will almost certainly run for the White House in 2016.
Two questions are:
Do voters take him seriously?
What about Clinton?
I think that after the past few years, voters accept him as a serious and effective candidate (despite the gaffes).
However, I think that if Clinton runs, Biden shouldn't bother challenging her in the primary. While I think he would compete well with any Republican challenger, he can't beat Mrs. Clinton in the first round.