UPDATE: This has been fixed in 15w32b. Video: https://youtu.be/2CcZTfdY0js
When fighting the dragon, it cannot die unless it is perched on the End Portal. Only tested with enchanted diamond sword (sharpness 5) in creative mode. Untested with bow or in survival mode.
More details: If you perform the final hit on the dragon while it is flying around, it will make the regular hitting noise instead of the dragon's hit noise. Once you hit it a singular beam of light comes out of its chest, staying there until it dies properly. If you hit it while perched, it will go through the regular death animation (may I also mention that the portal spawns above the existing one, but that's a separate issue).
I recorded a video of this here: http://youtu.be/elT-k0gh56o
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Dang, I looked for 10 minutes before posting this... Stupid search engine.
confirmed on 15w31b but i think it's normal
It is not normal. The enderdragon not dying when you kill it is definitely a bug. 😉
Still a problem in 15w31c for me.
Still present in 15w31c for me too.
Can confirm this still exists in 15w31c and that the same thing happens when he is hit by an arrow. I also discovered it is really hard to hit him with a sword and that the harming effect doesn't work on him, but the healing effect does.

Reopening
can confirm this in 15w31c
I didn't like the Dragon guarding the nest anyways. I like the old way ):. It was more challenging.
The not dying part might be intended; I see code that even includes a debug message "Dragon died whilst in the air, ignoring damage and going in to land".
I can't reproduce the light beam in 15w31c.

The dragon should promptly fly towards the portal and continue dying now.
This happens in 15w32a too.The Ender Dragon can only die when it is over the portal.

Does she not immediately start flying back to the portal to die?
Confirmed for 15w32A, tested it with the most powerful bow to man. And no. Also, the dragon seems to be taking random damage as well.
Can confirm this is not fixed.
I can confirm is not fixed yet
I hit the dragon with the bow when she is away from the portal, she returns to the portal constantly, but she doesn't die there. The only way to kill it is waitin for it to be on the portal.
P.S. Come on, Dinnerbone!! you can do it!! Don't let @Chincheto77 and @tonacho sing "Dinnerbone, Dinnerbone" with "Yesterday" lyrics everytime they find a bug on the game 😉

Indeed not fixed yet. She can only die when above portal (if you hit here).
She'll fly back to the portal after reaching 0 health but she still won't die until she takes another while hit while above the portal.
I can confirm that this has finally been fixed. If the dragon gets killed elsewhere it will begin blowing up and dive-bomb for the portal, then when it is above the portal is finishes the death sequence. Confirmed fixed finally! Thanks Dinnerbone!
I made another video showcasing the fixed version here: https://youtu.be/2CcZTfdY0js
The crouch button is transparent so it takes a few taps to stand up try and make it like jump button
Duplicate of MC-83191, but this description is much more detailed (and also includes a video).