How high can Minecraft spiders jump?

Solution 1:

I always put my lip just high enough so that I don't bump my head on it (that is, with 2 blocks of air between the ground and the lip). I have watched it stop spiders and have never encountered a spider above the lip. James' answer is correct about the spider AI.

Solution 2:

While they can jump, I am not sure of the height to try and give you a value (The wiki is empty)

What I can speak to is that the spider AI will generally walk forward and then jump up when it needs to, resulting in them being Under the lip and hitting their heads on it. While they can jump up to the lower ones, it would be a timing issue whether or not they made it.