The one I read was Katawa Shoujo. It's NSFW at a few points but has an amazing storyline. (Though you can disable the NSFW stuff in options).
It had multiple choice points that allowed you to pick any of the main characters. It was really cool because the choices you made changed the characters
kamisama kiss sounds like it has an interesting storyline. I looked at the wiki but it' seems to have a lot of details.