What is the average distance between objects in our asteroid belt? We've all seen sci-fi movies with asteroid belts that require "great skill" to fly through, but how dense is the asteroid belt really? 
How much of the belt could you see from the surface of a given asteroid? 
Is it uneven, with dense and sparse patches?
 A: 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.
A: Dr. Marc D. Rayman, Chief Engineer of the Dawn mission, gives some better statistics and analogies here: Dawn Journal: November 27, 2009

Dawn will travel 7.7 astronomical units (AU), or nearly 1.2 billion kilometers (almost 720 million miles), to its July 2011 rendezvous with Vesta. Yet in all that time, and across all that distance, the closest the probe will come to a catalogued asteroid is 1.0 million kilometers (greater than 600 thousand miles), or more than 2.5 times the distance between Earth and the moon. 

The set of cataloged objects ranges down to typically a few kilometers across, with some as small as about one kilometer.  But he also notes that Dawn is in fact prepared to hit some small particles.  Since they are travelling in the same general direction as most objects, the relative velocity will be low and they have protected sensitive parts of the spacecraft, so collisions are not seen as a serious threat to the mission.
I'd still like to see some more details on how big a particle they can hit and what the risk actually is.  These references may be of use, and suggest that there is still a lot of uncertainty in even what the right power law value is for the more risky smaller chunks and particles out there:


*

*On the asteroid belt’s orbital and size distribution, 
Brett J. Gladman et al 2009

*Asteroid Size Distribution - Sloan Digital Sky Survey

*The Collisional Evolution of the Asteroid Belt and Its Contribution to the Zodiacal Cloud - Daniel D. Durdaa and Stanley F. Dermott, 1997
And here is another fun related pdf, with a cool picture of the debris of an asteroid collision, and calculations on density and frequency:


*

*Hubble Spies Colliding Asteroids!
A: It all depends on the size of the asteroids that you're talking about. The asteroid belt in our solar system is so vast that even if you go down to ~1-meter sized objects, each one can have over 4000 square kilometers all to itself.  And that's without factoring in the fact that the asteroid belt has a third dimension to it.
But, there are clumps, "families," and other inhomogeneities to the belt.  Some asteroids do generally travel together, but they are still very spread out relatively speaking to what you see in movies and TV shows.  The main exception would be cases of asteroids with moons, such as Gaspra and Ida.
Here's a link that goes through some of the math.
A: The analogy my freshman astronomy teacher used was if you scale the average-sized asteroid down to the size of a potato, then the potatoes would be about a kilometer apart on average. 
A: Wikipedia estimates about 1.5 million asteroids in the main asteroid belt that are larger than 1 km (about 0.6 miles). With the total volume of 13 trillion trillion cubic miles given above, that would about 8 million trillion cubic miles per asteroid. Taking the cube root of this gives a typical separation of 2 million miles, or about 8 times the distance from the Earth to the moon.
A: Asteroid fields, as depicted in SciFi movies, are not stable. Over time, they would either dissipate, all those pieces of rock slowly floating away from each other; or, if they are big enough, they would collapse gravitationally and form a loose heap.
Dense aggregation of rocks, as shown in the movies, are not impossible. Some kind of low-probability collision event may produce them every once in a while, given how big the Universe is. But if you ever encounter one in your cosmic travels: first off, it's a highly unlikely event; and secondly, they are pretty fresh creations - take a good look, because they are going to dissipate in a blink of a cosmic eye.
A: To put it simply, every sci-fi movie that ever featured one does grotesque disservice to what an asteroid field is really like. In fact, an X-wing pilot, for instance, rather than having to swoop and dodge, would probably have a difficult time telling that he is even in an asteroid field.
I'll also endorse Stuart R.'s link working through the math, reproduced here.
