Is there a drama where the guy is a player/playboy/womanizer and falls in love with a girl?
Oh Wow. I've watched close to 120 dramas(mostly Korean) and not a single one came to mind. Leading men are not usually players... but here are some that I thought had some player like qualities. 
Heart to Heart
Marriage Not Dating
Personal Taste 
I Need Romance
Take Care of the Young Lady
A Gentleman's Dignity
Oh My Lady 
Playful Kiss
Flower Boy Ramyun Shop
That Winter the Wind Blows
I second A Gentleman's Dignity, as well as Playful Kiss (only as @kdramasinpajamas says, it's more that he has player qualities -- women find him very attractive -- but he's not exactly a player since he doesn't actually flirt with tons of girls ;) )

(the ones with a + mean that it's really a strong aspect of the story)

Autumn's Concerto +
MARS (a "bad boy" a lot of girls have a crush on)
ToGetHer (kinda, since he's a celebrity and enjoys his popularity with girls)
Que Sera Sera (he's worse than a player, dating rich women is how he earns a living haha) +++
Last Cinderella (not nearly as bad as the previous character, but a bit similar) +
Devil Beside You +
Full House (I have never finished any version of it, but have watched bits of the korean and the thai version especially, and in the lakorn I think he really was a womanizer)
City Hunter (a little bit, although not central)
Yamato Nadeshiko Shichi Henge (sort of: women adore him, but it's against his will...)
I third AGentleman's Dignity
Mary stayed out all night
Secret Garden-the second lead is the playboy there.
i second Autumn's Concerto 



i think some of the suggestions given aren't bad boy or has play boy qualities. In Personal Taste, The lead guy isn't playboy at all. Instead he was mistaken as a gay by the lead girl because he was always with his best friend slash his business partner. The lead guy in Take Care Of the Young Lady isn't a playboy as well. He worked as a gigolo before but it was in the pastbevause he had a reason to do it.
I 4th a gentleman's dignity!
Coffee Prince
Let's Eat
If I remember right Oh! My Lady and Birth of a Beauty.
There's Yi Jung from Boys Over Flowers but he's not the main lead