1995-1996 Apocalyptic mecha anime. Possibly intentionally subverting the mecha and harem genres. Very popular. Apparently a classic that shaped the medium.
First attempt (2012)
I'd heard about it occasionally, and tried watching it in the first half of 2012, but after a few aborted attempts to get through the first episode and it not gripping me (as well as multiple elements typical of anime irritating me) I didn't watch any further. Maybe I'll pick it up again.
Second attempt (25th November 2013 - 4th February 2014)
After watching a bit of anime in 2013 and exploring r/anime etc, my interest in Neon Genesis Evangelion was revived and I found I wanted to give it another try. I watched the first 2 episodes on the 25th of November and found them to be quite interesting, really, if you let the annoying aspects pass you by.
As of December 1st I'd watched 10 episodes, and felt like it was a bit simple and childish. Each episode had a sort of bland little 'adventure' with the characters essentially somehow getting into a fight with their Evangelions and managing to win at the last second or whatever. It hadn't deviated from that formula for a while and I was starting to lose interest.
I watched 3 more episodes before dropping it over Christmas and New Year, then in February 2014 I picked it up again and watched from Episode 14 to the end (including End of Evangelion) in a few days. I'd read more about it and got the impression that by the end it would be sort of amazing and so was worth persevering with.
I wasn't sure what to do about the 'Rebuild' remake movies but r/anime was clear I should not be watching those first.
The ending was... well as I've found out now infamously weird and hard to interpret. However, one post I found made the case that the writer, who is known to have suffered from depression, was just trying to subvert and deconstruct all the tropes that had become the norm, and that there really is nothing more to Neon Genesis Evangelion than the tale of a variety of essentially fucked up people and how they'd realistically get on in a typical story scenario. I like that theory, it makes sense of what I saw.
1, but only really because it had enough good bits, and because I'm told it's so influential, and because it was at least true to its vision and not at all cliché.