There are a number I really enjoyed. "Miracle Girls" was about a pair of twins with telepathy, teleportation, and psychometry, and also their boyfriends. Both the manga and the anime are worth seeing, and this one is older than even me.
"Kamisama Kiss" was about a highschool girl who became the Area God of the Mikage shrine, and her gallant but grumpy, not to mention tall, muscular, and usually underdressed kitsune familiar (in mostly foxboy but occasionally giant fox demon form).
"Kanata Kara/From Far Away" is about Noriko, freshly transported to a fantasy world where she is the prophesized Awakening. Izark would really prefer to not be transformed into the calamitous Sky Demon by the dreaded Awakening (think Yatagarasu, but bigger than Australia and tripping on henbane), but even though his dormant dark energies surge in her presence, he cannot bring himself to kill this cute and hardworking young lady.