A binary black hole system, viewed edge-on. This pair of extremely dense objects twists and warps spacetime as the two black holes spiral in toward one another. Image Credit: Bohn, Throwe, Hébert, Henriksson, Bunandar, Taylor, Scheel (see http://www.black-holes.org/lensing) via: http://www.universetoday.com/116500/new-simulation-offers-stunning-images-of-black-hole-merger/
What, exactly, would happen if two black holes collided? They would probably merge to become one bigger black hole, but it would be extremely violent, producing enormous amounts of energy and sending gigantic ripples through the universe called gravitational waves. Amazing.