After a mob aggros onto you, then you punch the mob, it de-aggros for a short time. This appears to happen with all mobs except the Ender Dragon, slimes, magma cubes, ghasts, and neutral mobs with the exception of Endermen after initiating the staring behavior. Curiously, it also does not effect creepers, although they do experience MC-48532.
I've also noticed something peculiar about this glitch. If you hit a mob, and it de-aggros, then you hit the mob while it is de-aggroed, the mob with chase you as normal and will not de-aggro again after hitting it more. But, after hitting the mob, letting it de-aggro, and waiting for it to aggro onto you again, it will de-aggro after hitting it.
This may or may not be related to my other ticket, MC-48532.
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I can confirm.
Still an issue in 1.8 pre-release 3. Mobs will become de-aggrovated for anywhere from a brief moment to several seconds. I found this is the case in both single player and multiplayer.
Confirmed.

Confirmed for 1.8.1.
Can confirm, still an issue in 1.8.1 through 1.8.2 pre-4
Here are videos exemplifying the issue.
http://youtu.be/g4NA23GKuE8 (Zombie)
http://youtu.be/QqfQIkIiFT0 (Spider) [This was a test during daytime too, it forgot it was even after me... as if it's AI was reset]
http://youtu.be/EG7oCi9Z5I8 (Baby Zombie)
Joshua, thanks for the videos, they really help. But the spider one in daytime is inaccurate, as spiders normally stop attacking after a few seconds during daytime. Try it again at nighttime, but be wary that spiders' AI has changed in 1.8, making it so when it de-aggros, it will move forward blindly for a second or two then stop.
I also noticed a spider bug in 1.8 that applies to the wolf too. It is my report here: MC-49129. Somebody please check it out, nobody has viewed it at all and I reported it months ago.

Confirmed for
1.8.4 for Zombies, seems like the game runs there some code at the wrong place because the Zombie even started walking away, but stopped after realizing that the player is still there

MC-84342 confirms for 1.8.8 and 15w31c.
Still buggy. Confirmed for 1.8.8.
1 year later.
Still in 15w34a. It's more obvious than ever now with the Zombie animations, as you can see their arms go back to their "non aggro" position while you're attacking them.
Looks like this was fixed in 15w35b, finally.
Yeah, as of now, Mojang seems to have fixed this bug. Man, this bug was annoying.
Endermen are still broken though
Joel, Endermen are not broken. They are broken in a different way, you are talking about how they lose their speed boost after you hit them if you stare at them to attack you. They do not de-aggro after you hit them. This bug is indeed fixed.
Fixed in 36c
actually its fixed in 36a
Thank goodness this has finally been fixed
Still in final release.