I know a romance drama where there was no kissing. Hahaha.
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But I see you dropped that one.
Atashinchi no Danshi is great and also no kissing. Romance though toned down is very cute.
Skip Beat! no kisses. I'm sure because I've read manga few times and they made the drama stay true to the comic.
I know quite a lot of K-drama and J-dramas with few kisses but I mixed them all up so I can't be sure which one is which.
Maybe I Love Lee Tae Ri?
My Girlfriend is a Gumiho has only one very cute kiss, or maybe there were two?
Did Oh! My Lady had kisses at all? Maybe at the end.
I can't remember if Dal Ja's Spring had more than two kisses or maybe I mixed it with another drama.
Anego? I don't remember a kiss but I may be mistaken. I'm not too sure about this one.
Dream High, there was a kiss at the end. :)
On Air, only one kiss in one of the episodes near the end.