I like NGE, not so much for what it is, but rather for what it represents to me, personally. NGE was my first "serious" anime (my previous experience was limited to Pokemon and Yu-Gi-Oh!), so it introduced a heck of a lot of new concepts and ideas to me that I had never before considered:
* It is possible to coat a serious, intricate plot with a heavy layer of action (and consequently make it more palatable).
* Good characters don't have to be likable.
* Imagery without meaning (all the crosses, etc.) still is pretty darn cool.
* Mecha don't have to be mecha.
* The more interconnected everything is, the more interesting a story ultimately is. This may seem common sense, but when you think about how NGE is actually Gendo's story, not Shinji's (similar to how Star Wars revolves around Anakin, not Luke), it becomes apparent that EVERYTHING somehow relates back to him.
* Negative human emotions and actions are more thought-provoking than positive ones.
* A good artist goes a LONG way in making a product cool. Example: Three of my
four NGE wall scrolls feature art by Sadamoto, and I really don't like the art in the original series.
* Quiet characters are intriguing.
* Classical and orchestral music do an excellent job of setting the mood you want.
** Corollary: Joyful music (like the Hallelujah Chorus) can indicate an...essence, I guess, rather than an emotion. I don't feel like that music is out of place at all in that scene.
* Making the viewer/reader/whatever think will be appreciated by them later.
I'm sure there's more, but the bottom line is this: NGE influenced my life quite a bit. I look back on the show itself and think it looks dated and ugly, and I'm tempted to say, "Oh, it's not that great," but then I look around at my eleven manga volumes, four wall scrolls, 2.6 gigs of pictures, the common theme of most of my desktop backgrounds, the only AMV I've made, the story I'm writing (whose genesis was inspired by NGE), and the only anime-related forum that I post on, and it's clear that there must be SOMETHING special about it.