Like the person above my two favourite family dramas are:

What Happens To My Family 
Reply series (particularly Reply 1988)

Reply 1988 and Smile, You
Any of the Reply series, but especially Reply 1988!
Smile, You
Five Children 
Reply 1988
Ugly Alert ... One of the best
Family's Honor ... Underrated, same author as Ugly Alert
Smile, You .... ROFLMAO funny!
The Legendary Witch
All About My Mom.......To Be A Better Man.........everything else seemed to be mentioned so far......unless you want things that are really melodramatic included........or series that are over 100 episodes.
What Happens In My Family
Ugly Alert
My Daughter SooYoung
Reply 1988
Five Children
OJAKGYO FAMILY AND SMILE YOU. THIS TWO DRAMA VERY FUNNY AND HILARIOUS!
As for me, I loved Family Honor, liked Five children.
Father is strange which is airing now is quite good. Its my first weekend family and i'm really enjoying it.
only k-drama? for me on family theme, tdramas are my favs, among them Dear Mom, Better Man and Love, Now are the best ones for me
A Daughter Just Like You - funny, 120 episodes though but still an ok watch