Eva spin-offs you wouldn't mind being made

It should be a spin off based on The Shinji Ikari Raising Project and they should still have shinji as a pervert

Rebuild of Rebuild of Evangelion

Evangelion: The nordic adventures.

Evangelions: Nordic Longboats with a soul type thing
Pilots: captains of each ship.
A.T Field: Generated by the longboats and controlled by nord warlocks (who also allow the pilots to keep in touch with their CO's).

This would be awesome.

I would like to see a side-series that spans the same timeframe as NGE, but from Asuka's perspective. What NGE is to Shinji, this series is to Asuka. The series begins with Nerv-03 reacting to Sachiel's appearance in Japan, and the next six episodes cover Asuka's preparations before leaving for Japan. Episodes 8-26 cover the same events as in the respective NGE episodes, but with more emphasis on Asuka. We see Asuka on her date in Episode 15; we see Asuka wandering the countryside like Shinji did before winding up in the bathtub in Episode 24; we see everyone, including Shinji and Kyoko, congratulating Asuka before she says thank you at the end of Episode 26. We hear more of her thoughts and see more of her history through flashbacks. In scenes showing exactly the same thing as what happened in NGE... the camera angle is changed? Oh, and she gets her version of EoE, too.

I'd also like to see a Beginning of Evangelion movie, including the stuff other people have listed... the Katsuragi Expedition, the contact experiments, more of the college years. For some reason one thing I'm keen on seeing is Yui's dive suit, after seeing a screen capture of it on the Commentary Project.

And both the Asuka side-series and BoE should have circa 1997 animation quality.

On a less serious note... are you all familiar with the After the End audio drama? I'd like six episodes or so of a serious attempt at the suggestions given there, all mashed together. Just what would Rei and Asuka's excessively fan-servicing plug suits have looked like? What would a sedan, a bullet train, and a warship look like with an Eva aesthetic? While combining into a giant sumo wrestler? While battling the Black God's Angels on Mars, and then the Space Black God in space? With the Children occasionally ejecting from their Evas and battling in person as a sentai team? It'd work. In context.

A spin off that sheds more light on SEELE would be a good one, also the misadventures of Aoba.

Rei Ayanami: The Movie (lol lame name) - A two hour animated film focusing on Rei's daily adventures in Tokyo-3 and revealing some of the more ... ummm, intimate details about her life that we don't know about. Does she snore? Does she wet her bed? Does she keep a pair of Gendo's unwashed underwear under her bed? Is she ticklish? What else goes on in her apartment when she's alone? Those are among the many things I'm curious about.

Rei Ayanami vs. zombies

Baby Asuka - I just want to see Asuka as a baby ; seeing her as a little girl was not enough, I want new-born, weeks-old Asuka.

Gendo Ikari's day off

Toji becomes a pro-basketball player, on account of the manager being an amputee fetishist.

Hikari shamefully and steamily degrades herself before corrupt corporate executives to get the highest rated cooking show on TV.

Kensuke and his intrepid camera crew go into a dark forest to do a documentary on a local legend about a witch, but discover it was only the boring old teacher, who is now a senile drag queen.

You Can (Not) Overtake: Asuka, Shinji and Rei are let loose on Fuji Speedway, seeing as Suzuka Circuit would be submerged after Second Impact.

I'd like to see a video game (WITH SOME EFFORT PUT IN) following the narrative that adapted the various other spinoff materials (Girlfriend of Steel, the various Manga, Rebuild, etc.) along with the original show to give us a distillation of the story in a new form. The game should be in the style of Zone of the Enders-style robot fights.

Failing that, I'd love to see the Eva cast in Silent Hill.