Here is a list of my favorites out of ~50 dramas I've watched.
My Girl: It gets angst-y in the last 4 eps but there are a lot of fun and heartwarming scenes in the first 12 eps which kind of made up for the flaws for me - you might feel differently. The chemistry between the leads is off the roof. Another Miss Oh: If you can get past the OTT and slapstick humor; quirky, OTT and irritating supporting characters, this is a very good drama. One of my favorites. Chemistry is again exceptionally good. A Gentleman's Dignity: Nothing much to say except that I wished a certain couple (not the main one) had more screen time. The Vineyard Man: One of the best dramas out there. It's lighthearted and there are a lot of heartwarming scenes. Full House: My first K-drama. Good but I don't like the cliff-hangers in some eps and the lead characters' immature-ish behavior. But their chemistry makes it a fun (albeit slightly angst-y) watch.
Marriage Contract: Very good, it could have been better without some of the elongated crying scenes. 90 Days, Time to Love: Not everyone's cup of tea. This drama is more about the characters who are very flawed people than the plot. Despite being a melodrama it managed to portray complex emotions and complicated relationships in a realistic manner. But it gets messy. The characters, the story and the physical fights are all messy and unsettling which for me was a good thing considering the plot.
Mature (as in realistic, not about sex)
Alone in Love: One of my all time favorites. If you like realistic dramas about realistic (and flawed) people with great story telling, down-to-earth characters who you can relate with then watch this. The humor is laugh-out-loud funny without ever being OTT. There are a lot of things I like about this drama but the humor is something I haven't yet seen done better. Witty humor and clever dialog make this a treat to watch.