This is a scene that is repeated over and over again in movies, books, games and any other area where science fiction has a place. Our protagonists are in a ship, it's being pursued hotly by some alien doom vessel trying to destroy them, and their only chance at escape/survival is to dive into the asteroid belt and hope that the alien pilot can't keep up with the many collisions and flying rocks! Basically, flying through a scene that looks very much like this:
This scene has one very large mistake in it: space is very, very big. There are two consequences of this; the first is that it is unlikely that one will find an entire asteroid belt that is full enough of rocks to have this scene at all, but there will be more on this later. The second consequence is that most space flight "chases" are going to be taking place with the ships light seconds apart, with the chasing ship firing, and then waiting to see if the shot hit or not. There is a small subset of people who might enjoy that type of scene, and this is the type of person who likes submarine thrillers; who waits on pins and needles to see if the shot fired hits and if the ship was detected soon enough for the enemy to get their own firing solution. But for most people, having 20 minutes of movie waiting to detect an explosion five light minutes away would be pretty boring.
The truth of the matter is, although the asteroid belt is a comparatively densely packed part of space, there just aren't that many rocks in there. The entire asteroid belt of our solar system is only 4% the mass of the Earth's moon! Even more interesting, more than half of the total mass is contained in the four largest asteroids. What this means is that a spacecraft is not very likely to find an asteroid, let alone have to dodge around one. According to Alan Stern of Space Daily, there is a less than 1 in 1,000,000,000 (billion) chance that a ballistic trajectory satellite would hit even one of them when passing through the asteroid belt. To give some perspective on the amount of rock this is, if one were to smash up all the rocky planets in the solar system and place them in the asteroid belt, there would be 10,000 times as much rock as is in the belt right now. This would only bring a ship up to a 1 in 100,000, chance of hitting something when passing through the asteroid belts, assuming that the size distribution was similar to what it is now, and that the ship doesn't dodge. So, the odds of hitting a rock in the asteroid belt with a ballistic ship are similar to the odds of throwing a rock in the ocean and randomly hitting a whale. This would seem to be an unreasonable amount of rocky material to have in a single system. Real asteroid belts are hard to tell apart from the rest of the system from the inside.
So, the moral here is that if a chase scene of this type is needed, have it be near a planet. Maybe a moon broke up, maybe they've been dragging rocks nearby for mining purposes, maybe the planet just has unusually thick rings. But having an entire asteroid belt this dense is over the top.