Is there a limit to how many blocks that an Enderman can traverse (either laterally or vertically) with a single teleport? Or is their teleporting radius essentially unlimited?
Edit: The wiki article on Endermen was updated with the following statement:
The range in which an Enderman can teleport is 32 meters in most cases, however informal testing on superflat worlds shows they can travel much further on the Y axis.
While this is quite ambiguous, a 32 block horizontal teleport distance seems accurate from my experience with Endermen teleporting.
Endermen will never give up a chase once made hostile; even when moving several hundred kilometers from them they will continue to follow until killed or distracted by exterior elements such as water or rain.
I presume this means that there is no limit to how far Enderman can teleport. However, because the Enderman would have to exist in order for it to teleport to the character, I believe that if you somehow get 128 blocks away from a hostile Enderman (causing it to despawn), the Enderman won't teleport to you. (If it somehow stays loaded in memory, it would still be able to teleport, though.)
a enderman can teleprt 64 blocks when attacked