I would have to agree with Synaesthetic that the anvil dropping in NGE was a pretty blatant thing and the plot was kinda weak.
But here's what I think coming from someone who has watched the tv series and movies multiple times and would like to see the new ones
Yes, I even like the TV ending
The "depth" isn't where some might think it is. Ignore all those Christian symbols for a second
A lot of people like to bash Shinji for being a wuss, and being a failure. Hell, I do it in jest sometimes too, just because Anno seemed so insistent on it. But let's consider the standard cliche hero for a moment. Shinji acts that way because he's just a kid that was yanked off the streets quite literally. If you had Shinji all hot blooded and GAR, ready for blood, that wouldn't come off as normal. In fact, that would make him a psychopath! So yea, I think Shinji cries and Shinji moans because he has a conscience. This is most evident when he is ordered by his dad to possibly kill his friend.
By the end, Shinji isn't emo; he's actually gone insane. The things that helped him keep sanity-- other people-- were slowly taken away from him. Then he learns his entire mission was a sham. And with that, he simply completely breaks down.
The point was that, no, you can't just put a poor kid in and hope he wins because he is the main character. And for its time, it was something new.
And interestingly enough, Asuka's more like the traditional hot blooded hero. If Shinji and Asuka were switched genders, you'd get a pretty ordinary story of a hot blooded hero and a pitiful partner that needs saving. But Asuka's case gets deconstructed, as we see what happens to the ace who suddenly loses potency and thus confidence, because as we know, hot blooded characters are fueled by this confidence.
While the plot is pretty obtuse when it comes to these things, it is the playing around with the psychology of these characters that made it memorable. And yes, I would think a lot of it is really just Anno getting over depression, but it's still an interesting study of that area.
I hope some of that made sense to those who got confused or just apathetic. Or at least offer another perspective with something less abstract.