 If you liked
Kure-nai
|
 ...then you might like
Boku dake ga Inai Machi
|
Both stories are focused on the MC being tasked with saving or guarding a young girl.
Both main characters have a super-human ability of sorts that really just functions as a plot device.
If you enjoy the "bodyguard" style of show, both of these shows are great examples of that genre being done right.