Any where it deals with the FL falling for the ML and having a normal relationship with him, but they have to deal with the entertainment world and all the problems with it. Her popularity and the people in it hinder their relationship.

  • Come and Hug Me | She's an actress, he's a detective. Though the story revolves more about healing their scars and dealing with a deranged serial killer than scandals of the entertainment world. You do get to see how the mass media portrays their story, though.
  • The Greatest Love | both ML and FL are actors. However, ML is in a much higher level of fame than the FL, so they do touch upon the issues of his fans not wanting them to be together as a couple.
  • You Who Came from the Stars | She's an actress and he's a... alien.
  • Lovely Horribly | Ongoing, this one is the other way around. He's a famous actor and she's a screenwriter who's trying to make meet ends. There's a supernatural element to this one, where their fates are entwined to the extent that... when something good happens to him, FL gets hit by misfortune. When something good happens to her, he gets the misfortune. It's really interesting so far.
  • Queen In Hyun's Man - the FL is a top actress, the ML is a noble from the past (i.e. an accidental time traveler), but other than that he's normal / human
  • The Producers - the FL is an idol singer "ice princess" and the ML is a regular guy; I dropped this drama so I'm not sure exactly how much romance there is or how much her popularity hinders their relationship
  • Come and Hug Me +1 (in addition to dealing with the entertainment industry because the FL is an actress, they also have to deal with the media because of the leads' relationship with a serial killer)
  • You Who Came from the Stars +1 (although on top of being an immortal alien, he's also a popular, wealthy, and very well educated professor)

and maybe:

  • My Only Love Song - the FL is an actress who accidentally time travels to the past, the ML is a poor conman from the past, but they don't really have to deal with the modern entertainment industry

The Eccentric Daughter-In-Law -idol falls in love with her fake spouse for a variety show she is filming. 

Kleun Cheewit -A lawyer falls in love with an actress who he believes killed his fiancé. It's a thai drama so the story isn't nearly as simple as I made it. 

Leh Lub Salub Rarng- Actress and a special units police officer fall in love after they switch bodies. 

In addition:

  • Star's Lover - FL is a popular actress while ML is part ime professr and partime ghost writer
  • That Fool - with the contract relationship plot between the FL who is a popular star and the ML who is an oddball office worker oddball nice guy
  • Tokyo Sun Shower - FL is an actress and ML works in  sushi resto
  • 99 days with a super star - FL is a star while ML is a bodyguard
  • Positive Physique - FL is an actress and ML is an aspiring director who was an ex
  • On Air - FL is an actreds while ML is a former manager
  • Game Maya - ML will become the bodyguard of FL who is a popular actress to get to the hottom of who is responsible for his fiancee's death
  • Nang Rai Tee Rak - FL is a supporting actress while ML is  policeman
  • Idolmaster.kr - though the romance was not fully developed between a FL who is an aspiring actress and the producers who wants to create the next IT girl idol
  • Mina 

20th Century Boy and Girl is EXACTLY what you're looking for. The FL is an actress and the ML is a normal guy who was her childhood best friend. She has to be on a show similar to We Got Married with the ML's actor brother (second lead) but the love triangle is really only one sided from the second lead, the ML and FL really like/love each other but of course the media comes into play. It's light, heartwarming and totally underrated. The OST is pretty amazing too!