These days, shoujo heroines falling in love with gods/yokai/etc. are all the rage. I think it's time to look back at the series that most recently popularized the idea.
KAMISAMA KISS (Kamisama Hajimemashita), by Juliette Suzuki. First published in 2008 and first published in North America in 2010.
PLOT:
Nanami Momozono is an extraordinarily unlucky girl. She's barely getting along as things are, but after her father runs off to escape gambling debts she finds herself alone, homeless, and penniless. A kindly old man takes pity on her, offering her a place to stay and a kiss on the forehead. Nanami couldn't have known that the old man was a stray Shinto god and that his offer was in fact a transfer of his powers and temple to her. Now Nanami is responsible for fulfilling the prayers of strangers along with a fox familiar who is as handsome as he is grumpy and who resents the new management.