Neon Genesis Evangelion is a fantastic anime series. Possibly the best. You can watch it over and over again and discover something new each time. But really, you have to examine it in two parts. In part one, it's essentially a "boy and his robot" story where 14-year-old Shinji Ikari has to pilot his giant mech from giant monsters called "angels". The second part of the series focuses on the crippling emotional problems he has with himself and his co-workers, Rei (the silent, cold chick) and Asuka (the hot-tempered, action girl) as the plot meanders towards possible apocalypse.
Suffice to say, the series has a lot of layers that are rooted in biblical mythology and psychological horror/art film shtick. You can enjoy it as a psychological thriller, as a romance, as a character study, and as an action series. But the ending... oh, the ending... the ENDING. Well, let's just say it leaves you... well, it leaves you.
Cue the fan fiction. People don't like seeing their favored characters die, seeing their favored characters end up with the wrong person (or no one at all), and they especially don't like things happening to their favored characters that make no sense. Everyone wants to know the three most important words a writer can hear: what happens next. So that's where all these people come in with either re-interpretations or sequels.
EVA-R is a bit of both. It introduces some new characters, builds on the old, and most importantly, stays true to the original material. It's a long story, and somehow, it's managed to build quite a bit of multimedia around it--fan art, manga, music, animation, and voice work... by the original (English) voice of a main character from the original series. I have no idea how this story got so much surrounding it. Most of the other places, I'm linking to the author's blog or web site. Now, I'm linking to a whole site.
It's not perfect by any means. It's written in a hybrid transcript/narrative format, it has weird branching storylines, and the spelling and grammar need a lot of work. Surprisingly, all the external material actually makes it harder to read.
Despite that, this is probably the best fan fiction for EVA fans that roots in the main mythology (meaning, it's about the main storyline, not a romantic pairing). The plot ties directly into the series almost seamlessly and continues onward giving the wanting fan what they want. Or at least one man's idea.