As @Krazer pointed out, your description matches that of the Korean manhwa series PhD: Phantasy Degree, wherein the female protagonist changes genders each time a ring is removed from her finger, as well as each ring having its own "personality."
From the link above:
A young, spunky, fearless girl named Sang is searching for the Demon School Hades. She runs into a group of misfit monsters who are all ditching classes from the same school. Sang convinces them to take her to the school ... and, since only monsters are allowed in, she 'monsterizes' herself by letting one of the misfits - a vampire - bite her. After the destruction of the Demon School Hades at the hands of the Madosa Guild in volume 3, she moves on to search for more of "Satan's Rings". She meets Chun-Lang, a young swordsman, who also has a Ring, and like Sang, can change genders.