In Minecraft 1.11 and onwards, the NoAI data tag now causes mobs to no longer be affected by Motion. This is a problem because it makes mobs basically immobile and impossible to move. (Breaking minigames, certain contraptions, etc.)

Basically, this is the inverse of https://bugs.mojang.com/browse/MC-96565, where NoAI first had its behaviour changed.

I thought the NoGravity tag was intended to replace this functionality.

What I expected to happen was...
The entities that have a NoAI tag set to 1 won't obey physics.
What actually happened was...
The entities with NoAI set to 1 would still obey physics.
Steps to reproduce:
Load up a world in 1.11, or snapshot 16w50a.
Get any mob, and use the command:

/entitydata @e[r=30] {NoAI:1}

The mob will freeze in place, and no longer be affected by motion.