(It says 16w05a but it's 16w05b, the bug tracker didn't have 16w05b and now it's archived. If a mod sees this, please remove it from the archived, as this bug is only due in 16w05b)
(I don't care if Searge said this is Works as Intended, I'm not ignoring this bug until it's fixed.)

As of previous versions and snapshots, NoAI would remove the entity's AI and make it ignore its Motion tag completely, however as of 16w05b this is not the case. The AI is removed, but the Motion tag is still obeyed.

Now please don't go ahead and quote Searge's

Any part of an entities behavior that is not implemented as part of the AI is not affected by the NoAI tag.

It's getting seriously annoying.

The no gravity thing anyway was forever here, and the chances of it being intended are 999/1000. Plus, if this removal is intended, the entire concept of NoAI is useless.

For the sake of making a good report and getting more interest, I'll use the normal report format;
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:
1. Open any snapshot or version between snapshot 14w32a to snapshot 16w05a.
2. In a normal world, use the command

 /summon Villager ~ ~ ~ {NoAI:1} 

(This could be most entities, but villagers are one of those that seem to work best)
3. Observe the villager/entity not obeying psychics (Not obeying gravity, punching/shooting it won't result in knockback, can't push it, etc.).
4. Open snapshot 16w05b or higher.
5. In the same world, observe the villager/entity obeying psychics (If the villager/entity is no longer there, spawn in another one. You can also use another normal world).