1. The Re-tuning of the World (RahXephon)

As they say, every ending is a new beginning, and you can't swing a dead cat without hitting some kind of anime series' "Reset the World" button. Ayato Kamina, instrumentalist of the RahXephon, fulfills the ancient Mayan prophecies, and re-tunes the worlds of both man- and muliankind, bringing the universe to a better, more balanced state.

Also, by re-tuning the world, he gets to marry his childhood sweetheart while not having to deal with her being twelve years his senior. Everyone wins!

2. The Destruction of Neo-Tokyo (Akira)

Call it narrow-sighted if you must, but in the eyes of most Japanese media, Japan is the whole world. And Tokyo is Japan. Mathematically speaking, then, ending Tokyo equates to ending the world at large. That's what happens to Neo-Tokyo in Akira, thanks to the combined catastrophes of Tetsuo's psionic rampage and the destructive strikes of the SOL Orbital Laser.

Death came from above and below, but hey, at least they had bitchin' motorcycles, right?

3. The Merging of the Worlds (Urotsukidoji: Legend of the Overfiend)

Urotsukidoji may have told the story of an apocalyptic dimensional merging, but for many people out in the real world, its advent signaled a cultural apocalypse as well. That's because Urotsukidojii was the pioneer of tentacle rape, a phenomenon that would forever change human perception of "That Japan-imation Stuff".  

 Once you see that stuff, you'll never be the same again. It goes for civilizations as much as individuals, really.

4. The Douze-Mille Attack (Gunbuster 2)

This one is more of a "near-miss", but it's impossible to ignore a humankind that would willfully destroy itself for the sake of survival. Like cutting off a limb to leave a trap, the forces of humanity turns the entire Earth into a massive warhead, the Buster Machine Douze-Mille, to throw at the last living Space Monster.

It's only by the timely intervention of Nono that Earth is spared this fate, which was a good thing, since it turns out that Guts and Effort, rather than planet-sized warheads, are enough to secure mankind's future.

5. The Last Love Song on This Little Planet (She, The Ultimate Weapon)

You can't talk about the end of the world without mentioning Saikano. It's one thing to pull the trigger on some kind of huge gun or detonate a giant bomb, but it's another thing entirely to maintain a relationship with the girl that ends the world. But Shuji and Chise manage to do so, and all humanity is better off for it.

That is, if all humanity had not been killed by Chise. Which she did.

6. The End of the Anti-Spiral (Gurren Lagann)

Another entry into the "near-miss" category, Simon and the Gurren Brigade take on the Anti-Spiral, the entity responsible for ending countless Spiral civilizations over, in an epic battle for the future of the universe. Galaxies are thrown, probability is altered, and the energies of the Big Bang are conveyed with every strike.

Had the whole thing not happened in a pocket dimension, the battle to save the universe would likely have annihilated it. 

7. The Ideon against the Ganda Rowa (Space Runaway Ideon)

The ending of Space Runaway Ideon is the very definition of "phyrric victory" in anime. Then again, is it a "victory" if everyone on both sides dies? Because that's what happened during that climactic final battle. The Ideon, the Ganda Rowa, Earth and the Buff Clan homeworld (both of which had already been devastated), and, well, everyone, gets vaporized by the last explosion, leaving their naked souls to rise into the next level of existence.

8. Emperor Lelouch gets impaled on a FABULOUS pink sword (Code Geass)

This destruction of the world is more symbolic than literal. The rise and fall of Lelouch vi Britannia heralds the ending of the previous, strife-ridden world order and the beginning of a new status quo, one that is happy, peaceful, and friendlier than ever to the concept of immortal green-haired women riding in hay carts while talking to invisible people who may or may not be dead.

9. Third Impact (End of Evangelion)

This couldn't not make the list. People scream, people get killed, people get eaten, and everyone turns into a puddle of delicious, nutritious Tang(tm) LCL. 

10. Madoka Kaname makes her wish (Puella Magi Madoka Magica)

(;_;)