Warning: Unless you've seen all 26 episodes of Evangelion, as well as the movies, you're in for major spoilers!
Ask any major anime fan which anime has the most controversial (or confusing) ending, and there's a good chance they'll say Evangelion. I don't think there's anyone who hasn't watched all of this brilliant show without feeling at least a bit confused as to its real meaning and a longing to know the truth behind many of the events that occur in it. So I've complied this page of some online resources that will help you better understand the incredibly complex, deep, and heavily philosophical world of Neon Genesis Evangelion!
John, from AnimeNation's Ask John Archive, is a fairly well known anime expert. He's answered hundreds of question that inquiring fans have about anime, so it's likely that someone would ask him what the meaning of Evangelion is. I think he explains it pretty well, so check it out:
Ask John - What is the meaning of Evangelion?
The following are a couple of questions that John answered regarding The End of Evangelion movie.
Ask John - Did Shinji do what I think he did(to Asuka?)
Ask John - What does Asuka's final line mean?
And, probably the single best site for Eva information, is the extensive FAQ page of EvaOtaku.com. I think it covers pretty much any question one might have about the series, so go give it a look see...
Well, I hope you find these pages helpful ^_^ Normally I write my own interpretations to the endings of anticlimactic anime like Eva, but I think these pages have everything already covered. But if you're interested in reading my opinion, I've actually written an over 30 page long Eva fanfic(a WYDS from The End of Evangelion.) Below is an excerpt from the epilogue of it, in which I've discussed some of my thoughts, particularly the conflict between Shinji and Asuka in The End of Evangelion movie...
"...I'm sure many think that the reason that Shinji strangles Asuka in the end is because he's upset with her and wanted to finish what he started(when he strangled her before, in Misato's apartment). I used to believe that, too, until I really examined certain scenes in the movie and realized that the first occurrence of Shinji strangling Asuka did not happen in reality, but was a figment of Shinji's mind created out of his frustration and incomplete relationship with her. I found that this was so because before we see that scene, we see the part from episode 15, where Asuka walks over to Shinji to kiss him. In reality, she ends up kissing him(and then regretting it afterward). But in this particular flashback that Shinji has, instead of kissing him, she yells at him and kicks him. Shinji's mind changed the reality of that memory because of the raging negative feeling inside of him at that time. Similarly, in the director's cut scene of episode 22(and in Death & Rebirth), we see a spilled coffee pot as Shinji is telling Asuka that Kaji is dead. So we know that that's where the spilled coffee pot really comes from. But once again, Shinji's tormented mind twists the truth in the movie, and we see the coffee pot spill when Asuka pushes Shinji and he falls, knocking the pot of coffee down in the process, before he starts to strangle her. Immediately after this scene, Shinji's mind begins to depict a bunch of random images of death. So as far as I can see, Shinji's mind at that time was rewriting his memories, making them seem more horrendous than they really were(and I highly doubt that in reality, Asuka would just stand there and let him strangle her). Also, what Shinji imagines Asuka saying to him in that scene("You're afraid of Misato and the First!"), is exactly what he said about himself at the very beginning of the movie. This further emphasizes the fact that the whole scene was wroughted from Shinji's frustration with Asuka and his guilt about raping her.
The reason that Shinji strangles Asuka at the very end of the movie is because he wanted to make sure that he was back in the real world...back in a world where pain once again existed and he was able to feel the presence of another again. This is the absolute answer given from an official Evanglion trading card. Shinji and Asuka were the first humans to regain their physical form and so Shinji wanted to confirm that he was back in the world where pain and other such feelings once again exist. But that still leaves an even greater question..what are they going to do? And what about everyone else? Well, Yui states that "...anyone can return to human form, as long as they can imagine themselves within their own heart." Since Shinji rejected the world in which all separate souls are one, the peoples' souls come back to Earth. So perhaps if they (the souls) are able to imagine themselves within themselves, they can become humans once again. As for what Shinji and Asuka are going to do is entirely open to debate. Obviously there's implications that they may be the new "Adam and Eve" but who knows? But I guess the real conclusion to Neon Genesis Evangelion is of the mind. It doesn't matter what's going to happen...all that matters is that they are alive. Two people who felt deeply for each other yet constantly hurt and rejected one another time and time again were brought together in a cleansed world and finally came to some kind of acceptance of one another. I think with a brilliant ending such as that, the details become meaningless :)