I have seen spiders (and other bugs, such as ants, grasshoppers, etc) fall very large distances without being killed. This morning, I knocked a spider off my wall (attempt to kill it), and it landed on the ground and happily scampered away. It probably fell 6 feet, which is incredibly far relative to its height. Relatively speaking, that spider's 6 foot drop is sort of like what a 1000 foot drop would be for me, isn't it?

If I fell 1000 feet, I would be killed. Even if I fell only 6 feet, I might be slightly injured. Why can a spider (and other bugs) fall so far without injury?

I believe it's because insects are so light. And some of them have very hard exoskeletons. Like grasshoppers - have you ever tried to cut one of those things open?

Impulse determines the severity of an impact.
Impulse is the change in your momentum over time.
Your momentum is your mass times your velocity.

if you have a large change in momentum over a long period of time, such as landing on a trampoline, it would be a softer impact then if it were a large change in momentum over a short period of time, say landing on a hard floor.

If we are talking about the spiders landing on the floor, then it is more of a question of having a smaller momentum. Because they weigh so little, first of all, the air resistance slows them down so they do not fall that fast, then when they hit the floor, they are not going fast, nor do they weigh a lot, so their momentum is very small, so hitting the floor only produces a small change in momentum (small impulse) so they do not get hurt.

dont let tarantulas fall off a table. they splatter.
we used to have a tarantula at our local junior high school, until one of the kids let it out of its cage and it fell on the floor.
it was quite gross.