Gotta second the Life Is Beautiful rec. I smiled through every episode.
I love this discussion since i love weekend family drama (usually have about 50 episodes). Some of them that are really good to watch are :

1. What happened to my family (A father sues his children to give them life lessons) ==> hmm this drama is truly beautiful and cover many aspects (family issues, love, comedy) truly great story and great cast

 2. Five Enough (A divorcé man with two children and divorcée woman with three children never thought of falling in love again but they end falling in with each other) ==> good story pacing, love the story of the two young couples

3. Father, I'll take care of you ( After their 4 children become independent, an old couple decide to live for themselves. One day, their 4 children come back to them) ==> Love the four main leads (those two couple really cute), great cast assembling, good storyline, and very neat and nice ending,

Those are really nice and heartwarming drama, please watch it if you have time :D
I'm waiting for upcoming kbs weekend family drama, My Golden Life (the writer from shining inheritance), i hope it will turn out to be great hehe
I hope this discussion will always continue, it is very nice to get info of good family drama from this discussion, thank you
1- Come! Jang Bo Ri ( the best EVER)
2- Reply 1988
3- Legendary witch
4- Unni is alive
Just finished watching My Father is Strange. It is a great family drama!

For me he best family korean dramas are:


1. Life is Beautiful (2010) - the best

2. Ugly Alert and Glorious Days

3. My daughter Sooyoung, Five Children, what happened to my family

4. Ojakgyu brothers, sons of sol pharmacy, dear my friends

Reply 1988 was a joy to watch 

Yeah Thats How It Is
Childless Comfort
Dear My Friends
Wang's Family

So far my favorites and best ones I seen are old  but this are the ones I still re-watch, make me cried and laugh. All have really happy endings too.

Life Is Beautiful 2010 - is just beautiful.

Family's Honor 2008 - didn't care for the main OTP, but loved the all secondary couples and I loved the all main family, such a beautiful and moving story, one of the best, great ending too.

Pure 19 - 2006 daily drama, funny, cute main OTP, loved the music and loved all the characters, specially the male lead's family. Is 167 episodes but the sub version is edited into 122 of 40 min or so instead of the normal 20-30min version, so it didn't felt that long for me, the longest drama I seen was 173.

Golden Bride 2007 - arranged marriage between a half Korean/half Vietnamese girl and Korean guy who is suffering from emotional/mental problems after an incident with his ex, the girl helps him through it and he tries to help her find her Korean dad who left her when she was a baby. The most skinship/kissing i seen between an OTP in family drama so far and I really liked the way the family cared for the female lead specially the mother in law.

Golden Era of Daughters in Law and I Believe in Love - same writer
GEOTIL - really funny, only cared for the second OTP story though, but still find it pretty good as a whole, I specially loved the last few episodes and the songs.
IBIL - didn't like the older son's story but loved the adopted daughter and the family's older cousin story the most starting in episode 4-5, some characters I find really annoying but ended liking them except one, really good ending too.
Thank you (true it's old but this is very beautiful and touching)
Golden rainbow 
I liked all about my mom :)) my daughter soo young was nice too

I have watched may daughter seo young and sons of pharmacy house. Both of them are really good family drama and included in 50 highest rated kdrama in all time... thumbs up  :D
I need more like this but i know not all family drama is great so i neep help for other review hehehe

Hooray for Love, Simply AMAZING! I loved every second of it :D

Also, Wonderful Mama is Another really good one, especially if you're a fan of Park Bo Gum, Kim Ji Suk or Jung Yoo Mi :) I highly recommend them both!

Five Children, absolutely. It has 54 episodes and it's amazing! I'm sure you'll love the storyline and the characters :) The main couple is so cute and their kids are adorable. Also the actors are very good! 

i have watched five children, yes it one of the best. From start to end is amazing :)

i'm really  interested with MinaVIP suggestion,  i will check it soon when i have  spare time... I love to see lee bo young and jung yoo mi family drama.
This group surely means a lot for me,  hahaha