The NASA Dawn mission sees a craft headed toward the Asteroid belt as we speak - they intend to do well, navigating to Ceres and Vesta, and more.
Our intuitive knowledge of the universe tells that there will be both semblance chaos and order, with bodies having dominating factors, creating mini, seemingly orderly systems which could or would eventually lead to collisions, but we can be sure there's a lot more space than there are objects.
The actual spacing between each of the objects can't really be known entirely, we don't even know of all the objects in the main asteroid belt; however, we can estimate based on the knowledge that we do have - the Dawn site also has some information on this, so to quote a concise passage:
Asteroids are not distributed
uniformly in the asteroid belt, but
could be approximated to be evenly
spaced in a region from 2.2 AU (1 AU
is 93 million miles, or the average
distance between Earth and the Sun) to
3.2 AU from the Sun and extending 0.5 AU above and below the ecliptic (the
plane of Earth's orbit, which is a
convenient reference for the solar
system). That yields a volume of
roughly 16 cubic AU, or about 13
trillion trillion cubic miles. (Note:
space is big!)
Standing on the face of an asteroid and looking into the belt wouldn't give you a particularly revealing view of the belt on the whole, in fact objects in space would seem somewhat sparse at that level. The further away from it you are (within visibility) and ideally from an angle above the orbital plane, the more of a picture you would build of it being a 'belt.'
Also, here is a decent read with some observational analysis on the asteroid belt’s orbital and size distribution.