Bleach, Japanese anime tv series 2004

Story:

Ichigo Kurosaki is a 15-year-old-boy who has an ability to see ghosts/spirits. Because of his ability, he is able to meet a female death god (AKA Shinigami) named Rukia Kuchiki. 

To save his family and friends from unwanted soul-eating spirits (Hollows), Rukia transfers her Shinigami powers to Ichigo. 

As Rukia takes on a human shell, together they solve mysteries involving spirits and Hollows until from the spirit world come two other Shinigami, who explain that it is illegal to transfer Shinigami powers to humans and that Rukia exceeded the time limit to stay in the human world. 

After they sentence her death for breaking the law, Ichigo snaps and swears to everyone he will retrieve Rukia by breaking into the spirit world.

External link: Official Website