Oh my god, guys! Who here say the new anime Boku dake ga Inai Machi? It's about a guy who, for as long as he knows, has had the ability to go back into time and stop things from going bad, although he can't control it. It just happens, and he has to stop the bad events from happening.
It's AMAZINGLY well made, and I think you'd like it very much! It has a Stein's Gate feeling to it, so if you're into psychological anime, BAM. You're not going to be disappointed!