Make a 4x4x2 hole with lava in it and place signs on top of the lava.
Now spawn a spider on the other side of the hole, and use a bow to make it aggressive.
The spider will try to walk "across" and fall into the lava even though it could walk around it.
This also works with zombies, (and other aggressive mobs I guess) and you can use fence gates instead of signs, but you would need to remove the lava.
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I believe this works as intended. It has been known for a long time that this happens, and the devs have probably left it in because a high percentage of mob farms use this technique to make them walk off edges. Fixing this would break about half the mob traps in existence.
Is this still an issue in the current Minecraft Snapshot 15w46a or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
Mob AI got updated recently.
This has likely been reported before but I am unable to find the report 😞.