There is a very big crash, shivers go out through spacetime, and you end up with a single, bigger black hole, usually spinning quite quickly.
This is a very exciting time for black hole research because within the last year LIGO has seen gravitational waves given off by these collisions for the first time.
One of the amazing things about these collisions is the amount of energy given off. In the most recent collision the black holes that collided were about 8 times the mass of the sun and 14 times the mass of the sun, and the final black hole was about 21 times the mass of our sun so about the weight of our sun was radiated away in gravitational waves. Remember Energy = mass *speed of light squared (E=mc^2) so that is a LOT of energy.
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