Exact figures for the number of asteroids in the asteroid belt vary widely, but astronomers generally agree there are millions of objects of at least one kilometer in diameter. That sounds like a lot, but it turns out the asteroid belt is a fairly empty and lonely place.
The average distance between main belt asteroids is just shy of 1,000,000 kilometers (600,000 miles). For comparison, the distance between the Earth and Moon is a little less than 400,000 kilometers (240,000 miles).
But for hotshot space pilots like myself, there are still some opportunities to zigzag between and around dangerously close asteroids, perhaps while being pursued by hordes of Imperial TIE Fighters.
Over a hundred asteroids are known to have at least one tiny moon. Binary and trinary asteroids have also been discovered. Those are pairs or trios, respectively, of asteroids of roughly equal mass that are locked into orbit around their common center of gravity.
And of course when asteroids collide, they often form debris fields. This debris can linger for weeks before recombining as a rubble pile asteroid. Maybe these chaotic post-collision debris fields are just the perfect place to try evading the forces of the Evil Empire. Assuming you can find one.
Links
10 Things You Need to Know About Asteroids from Time and Date.
Images of Asteroid Ida and Dactyl from NASA Near Earth Object Program.
Binary Asteroid from The Worlds of David Darling: Encyclopedia of Science.
Planet Pailly 
It’s kind of interesting how persistent is the myth in science fiction of a navigationally dangerous asteroid belt. You’d expect it in Star Wars (although they tried to weasel through it with the phrase “asteroid field”). But even a Star Trek:TNG episode had one. And I recall reading a Lester del Rey book where the hero had to sweat through the asteroid belt constantly adjusting course to avoid collisions, and a Robert Heinlein novel where people spacewalked between asteroids.
Of course, NASA has sent numerous probes through the asteroid belt without issue. It turns out intercepting an asteroid takes careful navigation. Although I’m sure they checked for possible near passes, more as a precaution to what the asteroid’s gravity might do to the probe’s course than out of any concern for a collision.
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I’ve read that NASA worries just a little every time a spacecraft passes through the asteroid belt. There’s no way to know how many as-yet-undiscovered asteroids there are. Even so, the odds of a collision are pretty low. Asteroids just don’t cluster together very often, and the ones that do turn into rubble piles.
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