It has never happened in my lifetime, but we have a shot at it this cycle. It is a situation where no one candidate has enough committed delegates to win the nomination going into the convention. This is more likely this cycle due to the compression of the schedule. If we have an equitable distribution of wins through Super Tuesday, things are going to get desperate. 29 states will have voted by February 6th (27 Republicans) including New York and California (including two states that have been stripped of their Democratic delegates).
I heard Tony Blankley of the Washington Times say that he has upgraded his hotel room at the Republican convention to a suite to allow for people to meet in there, should it be brokered.
We have already seen a number of odd voting events in the past few years (see Florida, State of) so why not an all-out political brawl at the conventions? Sadly, I think that such a situation on the Dem side would benefit Hillary, it is much more fluid on the Republican side, but it’s early. Either way, it is going to get interesting.