I've never liked Neon Genesis Evangelion. This isn't to say that I hated it or anything, but more that it failed to fully elicit any sort of severe response in any direction. I didn't hate it, and I didn't like it; I was just not interested in it.
Which, I suppose, is sort of the problem, and worse than active dislike of the series: Evangelion failed to interest me, and so the only emotion I drew from the series itself (distinct from the emotions I have towards the fandom, which ranges from polite attention to eye-twitching irritation) was boredom. The series failed to engage me at any level. I've been classified as a hater of the series because of this, which I think kind of misses the issue: I don't have the passion to hate Neon Genesis Evangelion. It's just there. You may as well ask me what I think about the cultivation of yams.
From conversations with people who are fans of the series, it appears that a common thread (but by no means universal) is the ability to identify with the main characters, most often Shinji. (Occasionally Asuka is held to be the identifiable character; sometimes Misato.) They see themselves in Shinji, and they can empathize heavily with what he is going through.
Or maybe not, and I am completely misunderstanding the situation. I can kind of see it academically, but I cannot quite grok it to the fullness of understanding. This is because the three main characters, Shinji, Asuka, and Rei, are thoroughly unidentifiable for me. About the closest character I can empathize with is Rei, since she's quiet and unassuming, but I hear that she's not supposed to be empathizable, so I apparently have been suckered in or something.
I'm pretty sure I was never like Shinji or Asuka. This is not a boast, since it's entirely likely that I was in some way worse. But I didn't have parental issues, and I grew up in a happy home environment. There is just nothing connecting me with people who went through what Shinji and co. did. It's kind of like a cultural gap, except not exactly cultural, but more circumstantial. I recognize that it is a valid personality type; it's just not mine.
I think the character who would have the same sort of reactions I would might be Maya Ibuki. Her actions seem kind of natural, at least.
And since I can't empathize with the main characters, my other option was to watch them from the outside, seeing how they act from the viewpoint of an invisible observer. Considering my usual tastes in comedy and lighthearted fun, however, Evangelion held no joy for me.
I can understand that it is significant to the culture of anime, as well as its enormous influence. But I just don't like it. This has no bearing on its quality or its importance; just my personal tastes.
I should probably be spending more time on this topic, but not only do I not have the time or inclination to do so, I also don't think there is anything more that has not already been said by many others far more eloquent than I am.