Could anyone give me some recommendations to some dramas where our main male lead is a celebratory and falls for a normal girl?

Full House  
Wannueng Jaa Pben Superstar ( Thai ) - Ongoing 
Bad Girls (  T - Movie )
Twenty Years Old 
ToGetHer
Kamisama Mou Sukoshi Dake
I asked a similar question once= http://mydramalist.com/discussions/recommendation-...
I second ToGetHer, Myung Wol The Spy, all You're Beautiful versions, Twenty Years Old and The Greatest Love (although technically she's a celebrity too -- just a very unpopular one)

And I'll add I Need Romance 3, Oh My Ghost (he's a star chef, and she's just a clumsy assistant) and One Pound Gospel (boxer and nun)
Trot lovers - He's a singer, she's a very ambitious marathon trainer (not for long tho). They have a bad start and he has to make a singer out of her (reasons). (Love-hate relationship Yay! *-* ) (the girl from Reply 1997 plays in it)
Jang Geun Suk's character is midly popular/locally famous in Mary Stayed Out All Night, the same goes for You're My Pet.
Lovely Girl also fits your criteria: idol (L) falls for song writer (Krystal)
Wow, thank you so much everyone 
Here are some dramas which haven't been listed yet

- Monstar
- About love
- Ai ore! Love me!
- Hana yori dango, Boys over flower (~)
- Kpop - the ultimate audition
- Last scandal
- Ma boy