I can't believe I originally read it this way...
Anyway...
Personally, I'd love it if an adaptation was made of Gary Landsman's famous fanfic "Nobody Dies". I do have my minor problems with this, but as far as an AU spinoff goes, this would be excellent.
A canon spinoff I would like to see is a one-shot. "A Day in the Life of Rei Ayanami", done in the style of "Freeman's Mind" (look it up on Youtube). A first person POV of the thoughts of Rei as she wakes up, does her morning routine, go to school, stares out the window, goes to NERV, goes home, then goes to bed.
Another spinoff I would like to see (that we actually did see a peek of) is the "slice of life" that was seen in Ep 26 (or was it 25). Something short, perhaps 3-6 episodes long.