I recently watched Missing you and I was in love with men obsessed in love with the main female. I saw obsessed the movie, chuno, boys over flowers, summer's desire,  the greatest love, a thousand years of love. It does not have to be Korean. I took a liking to Asian men. I live in America so I am new.
Missing you was what I want. I am now bored from seeing it alot. I hate obsessed women. I love obsessed men. They are better.

p.s. No historical dramas. I hate chuno.  Also, I do not like comedies when it comes to obsessive love. It has to serious matters.
By obsessed, I assume you want the jealousy and angst due to it... Not much of that in in K-dramas...Maybe:
--- Que Sera Sera

Tons of it in C-dramas (but u don't want historical):
--- Sealed with a Kiss ... He defines the Obsessed Male!
--- Too Late to Say I Love You .... Very obsessed, not a perfect hero,passionate love.
--- Loving, Never Forgetting ... well, she was obsessed, but he acted on it, he was jealous, possessive.

--- Meteor Garden ... Taiwanese BOF / HYD .... Ultimate obsessed Male!!! ...Possessive, passionate,  with all the jealousy, angst, etc...

Cruel Romance has what you're looking for. Huang Xiao Ming(from Summer's Desire) is the male lead too.

Summer's desire- two yandere guys obsessed with the lead girl

Bridal mask- the villain guy is the definition of psychopath

Falling For Innocence- the second lead is a yandere

Roy Leh Sanae Rai- the ML is a anti hero type

The thousand years of love- the villain guy is yandere 

Delightful Girl - the second lead is a stalker

secret- the ML is a stalker

Love never dies- the villain vampire likes the lead girl 

Cruel romance- the villain is a stalker and a psycho

Memory lost- villain is a stalker

Ngao jai- obsessed villain

The journey- u might like it cause two guys obsessed with the girl