I'm not a programmer, nor particularly good at advanced mathematics, so I'm quite clueless exactly how to implement it, although I've always thought of wrapping the image, both x- and y-axis...something like this...

(sorry about the small size, for some reason it resizes the image, even though it was only 640x480)
The greenish-yellow area in the centre of the screen is the normal view, and the white areas around it the extended view. The normal view does not have quite as much wrapping as the extended view.
I always loved the view in "Metroid Prime", even though it wasn't even near 180°, but it was still much better than the "flat" view in most FPS games, it felt much more natural due to the "visor view".
So, any ideas?