I used to think (not very clearly) that there wasn’t a whole lot of danger unless you were traversing an area whose circular orbital velocity was different from your own (e.g., you’re accelerating for a higher orbit, and just passing through). If you’re in an orbit like the one that the Shuttle uses, everything would be drifting along pretty much at the same speed you are, no worries. You’re only in trouble if you try the Frogger thing.
The problem is that there’s a ton (well, many, many tons) of stuff up there in highly elliptical orbits, and some of it is breaking up. So you can get whacked by something going many miles a second, from practically any direction. A fifty gram blob of radioactive coolant with a relative velocity of 10 miles/second would ruin your whole day.
I don’t know what you clean this stuff up with (nano-bots that stick solar sails onto the small debris? Smart aerogels, kilometers wide, that sponge up everything that hits them? There’s too much volume to cover). In all probability, spacecraft armor will be standard eqiupment for the next few thousand years.