Nurse Christine Chapel, USS Enterprise, NCC-1701
Other than providing an unrequited love interest for Ol' Pointy Ears, it is hard to see what this character did, other than shrieking "Dr. McCoy!" (and providing a job for the wife of the creator/executive producer of the show). The character was at least a little more significant than Yeoman Janice Rand, who seemed to be there solely so that Kirk would have someone to leer at.
Transporter malfunction beams her into the warp core.