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It is believed that, during the first million years of the solar system history, planets formed by accretion of planetesimals. Ripetute collisions led to the familiar rocky planets and to the gas giant's cores.
However, in this zone of the system the strong gravity of Jupiter inhibited the final stages and the planetesimals could not form a single planet.
Collisions between asteroids occur very often (in astronomical terms). A collision may fragment an asteroid in numerous small pieces (leading to the formation of a new asteroid family[?], or may glue two asteroids together if occurs at low relative speeds. After five billions of years, the current Asteroid belt population bears little resemblance to the original one.