The word "yandere", a term that refers to a character that is literally crazy about someone else, to the point that they may be considered mentally ill. On the outside, the character seems Moe, but on the inside they are obsessive, controlling, and sometimes just insane. This may include jealousy of anyone else the target of her affection talks to, stalking, being violently protective as well as domestically abusive. Sometimes, if the LoveInterest ever starts to rethink his relationship with this girl, she might threaten to harm him or even herself if he ever leaves her.
A possesive yandere may be so in love with her crush that she's willing to kill her beloved to prevent other love interests from taking him away from him.
An obsessive yandere may be willing to kill off her competition so she can be closer to her loved one.
Contrast with Tsundere, a female character who often acts cranky, but harbors a hidden sentimental side. At the extreme, ALoveToDismember can occur.