The distance between things in orbit is vast, and Earth orbit is a huge place. Put simply, the chances of any two things colliding is very, very slim despite there being thousands of active satellites in orbit and many more pieces of smaller space debris because there is just so much space between everything.
However, another reason is that most of our manmade satellites travel in similar orbital bands at similar speeds within those bands. This means they’re moving in the same direction at specific heights, sort of like an imaginary conveyor belt moving around Earth. There’s not really much chance of one satellite catching up to another and, even then, the chances of a collision are low.
The only major risk to something like the ISS, which is 420 kilometres (260 miles) high in Low Earth Orbit (LEO), would be if someone decided to launch a satellite into orbit in the opposite direction to the space station at the same height, which isn’t really possible thanks to orbital mechanics; most things (aside from satellites in polar orbits) move the same way Earth rotates to get an added speed boost at launch.
Of course, though, collisions are not unprecedented. In February 2009 an active American satellite collided with a defunct Russian satellite, destroying both and creating thousands of pieces of debris larger than 10 centimetres (four inches). Thankfully a lot of debris of this sort will eventually be pulled into Earth’s atmosphere and burn up on re-entry, although some debris does remain a threat.
Image credit: ESA