ChäoS;HEAd, Higashi no Eden Recommendations
Both are mysterious and main character must save the world.
Both Higashi no Eden and Chaos Head have a main character who is thrown into a difficult situation with no recollection of their past. They both have the ability to change the world. Higashi no Eden is slightly more realistic while Chaos Head has a lot of supernatural elements, but they both take you on a short 13 episode suspenseful joy ride that just leaves you hungry for more.