A boyfriend/girlfriend or possibly someone who likes you who becomes let's say, obssesed. Signs that your boyfriend/girlfriend is clingy: doesn't stop calling, constantly tells you how much they love/like you, writes you songs, buys you flowers/chocolate so much it gets annoying, and wants to spend time..all the time.
For serious cases they may begin talking about moving in, or marrige after only a month!
Sally:When I first started dating Bob it was ok..but now..he's always around me, my answering machine is never empty, and he's best friends with my mom!
Sally's friend: Damn that's clingy!