Comets are made of ice, dust, and small rocky particles (somewhat similar to a gigantic dirty snowball). The size of these comets can range from a few hundred meters to a few kilometers across. Given the large expanse of empty space in the solar system, and the relatively small size of the comets, a collision between two comets would be pretty rare. Such collisions are so rare that, to my knowledge, there has never been a record observation of comets colliding with each other! So, I can only guess at what might possibly happen in the event of such an explosive collision.
There are two situations that would most probably happen--these are just purely educated guesses on my part.
Situation one. A head-on collision. The comets would most probably disintegrate into smaller pieces. In addition, the large amount of thermal energy produced by the collision may be able to vaporize the ice into gaseous water, and may also produce glass particles from the melting of the rock particles.
Situation two. A sideways collision. Think of this situation as throwing two snowballs in roughly the same direction, but being very close to each other. Once again, this scenario is purely a guess on my part. Some of the ice and rocky particles would come off the comets. They may even attract each other in such a way that they reform into a larger comet. Or, they might just "bounce" off each other and go their separate ways.
(published on 11/20/2011)