Variety / Drama

Need to have a lot of funny moments

--My list is not updated on what I've watched, sorry--

I am not sure if there are other dramas that have a lot of funny moments in every episodes. But I think The Sound of Your Heart fulfill your requirement! :)
High Kick Season 3 I was unable to stop laughing
I am plannning to wath season 1 and season 2 too I've heard they are as funny as season 3

and ( shut up family ) too they said it is too funny and comedy
I suggest:
The Lover - it is probably the funniest drama i have seen but it has specific type of humor so i am not sure if you will love it as much as i did. It is kinda realistic drama about relationships but at the same time it felt a little like series of (interconnected) sketches from SNL
The Boy Next Door - which is a really short series about two guys living together. The humor is very over the top but it's so bad that I found it actually fun :D
Reply 1997 - if you want to watch something that is not focused purely on humor i suggest reply 97. imo it has good balance of fun (i remember i laughed a lot!!) and captivating story (who is the husband?)
Chief Kim
Knowing Brothers
Running Man
1 Night 2 Days (my favorite is season 3, but if you have favorite comedians/members you can watch their season, i.e. season 1 for kang hodong, season 2 for cha taehyun's beginning, season 3 for kim junho, etc.)
Strong Woman Do Bong Soon (this one the main characters get serious, but the supporting ones stay comedic so their scenes are funny every episode)
I second Knowing Brothers. It's a must watch
Chief Kim, Strong Woman, WFKBJ