Binary solar systems -- systems consisting of two stars orbiting each other -- are quite common. Astronomers using the Spitzer Space Telescope have observed that many of them have a lot of dust and debris, leading to the hypothesis that the dust clouds were originally planets that collided with each other.
Geophysically, what would it be like if two planets hit each other? Phil Plait of Discover writes:
The energy in such a collision would dwarf the sweatiest nightmares of any Hollywood writer — or religiously-motivated apocalyptic preacher, for that matter. The two planets, each massing sextillions of tons, would ram each other at speeds of 20 or more kilometers per second. The energy released would be trillions of times that of all our nuclear weapons combined.
Link via Sci Fi Wire | Image: NASA