There are hundreds of thousands of asteroids orbiting the Sun. A few of them are larger than 200 kilometers (125 miles) in diameter, but the majority of them are about the size of a pebble. Most of the asteroids in our solar system lie in a thick belt between the orbits of Mars and Jupiter.
Even though there are many asteroids in the asteroid belt, flying through it isn't dangerous. It's not at all like the dense field of huge imposing spinning rocks like you'd see in movies. The asteroids are spread over such an enormously large amount of space that the chances of you hitting one would be extremely low.
Why would Hollywood lie to us like that? Because they want our money, that's why. And we are more than happy to give it to them.
I did some rough math during a caffeine-induced frenzy, and it looks to me as though within the asteroid belt, on average, there's a few million miles between one asteroid and the next. So, if you were traversing the asteroid belt, the chance of you hitting an asteroid would be similar to the chance of colliding with Elvis or John Lennon's accountant.
They don't even spin very fast. Most of the asteroids take many hours to make a complete rotation.
If you added up the mass of all of the asteroids, it'd be less than that of the Earth's moon. The solar system simply doesn't contain all that much asteroid stuff.
The bottom line is, you can completely forget about the asteroids and it won't disrupt your travel plans one bit.