Come and Hug Me | ongoing. Not exactly a bodyguard, but ML is a detective and the series revolves around him protecting the FL (actress and ML's childhood friend/first love) from a serial killer. Highly recommed it.
You Who Came from the Stars | MC is an alien who ends up protecting the FL (actress) in different ways. He ends up becoming his manager/lawyer/bodyguard.
Lawless Lawyer | again, not exactly a bodyguard, but ML does protect the FL throughout the series. He also has a bodyguard that he most times leaves with the FL.
Korean Odyssey | This one is urban fantasy. ML can see ghosts and gets a rebellious deity to protect her via a magic trinket.
Black | Grim Reaper possessing the body of a detective protects the FL who can see ghosts. Although at first he does it for convenience (he needs her to do something for him), later on he falls in love and protects her because of that.
Strong Woman Da Bong Soon | FL had super strength and ML ends up hiring her as a bodyguard.
Man to Man | ML is hired as the bodyguard for an action star (as part of his spy mission). FL is the action star's manager.
Mirror of the Witch | Fantasy. FL is a cursed princess and ML ends up becoming her bodyguard. 2ML (FL's adoptive brother) also acts like her bodyguard.