Asteroids can collide into each other. If two asteroids collide, the smaller one will explode. Collisions between large asteroid do occur, and these can produce an asteroid family whose members have similar orbital characteristics and compositions. The large population of the asteroid belt makes for an active environment where collisions between asteroids occur frequently. The chance of an isolated asteroid colliding with another is minimal.
For such an event to happen, both asteroids are generally under the influence of a gravitational field of a much larger body. Depending upon the velocities, masses and the angles at which the collision occurred, the asteroids could lose orbital velocity and eventually crash into the larger body. Depending upon the velocities, masses, and the angles at which the collision occurred, the asteroids could lose orbital velocity and eventually crash into the larger body.