Space [...] is big. Really big. You just won't believe how vastly hugely mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space
Space is big, like very big. And with different altitudes, inclinations, eccentricities etc (look up Keplerian elements if you're interested in the things that define an orbit) you could have thousands of orbits. Also each can be used multiple times in theory, ie you can have an object on the opposite side of another on an orbit, or anywhere else for matter.
That being said, the ISS does sometimes have to move out of the way of things, because most satellites are in Low Earth Orbit (below 2000km altitude having a max period of about 2 hours I believe)
So that's a massive area of space. But it is getting crowded. However that scene from the movie Gravity where everything just snowballs into total destruction of satellites and stations, that is very unlikely to happen
Because space, especially 3d is much larger than intuition tells you. What seems like tight trajectories are really spaced.
And satellites in the same height have the same speed and not very likely to hit each other
Because people also tend to underestimate how bloody large earth is. Surface area at 400 km high is over 2 billion square km. With roughly 300,000 items (which includes debris at 1cm^3) you still have lots of space between each object and thus chance that something hits each other is also quite low. Assuming everything was at the same height.
But it does need to be monitored because small pieces can have severe consequences.
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