If you are interested in any airing dramas that are ongoing, I would recommend these ones:
Another Miss Oh - very emotional scenes, super touching, and is ALWAYS interesting
Beautiful Gong Shim - very quirky, and just really well written
Some dramas I am currently making my way through that are really impressing me:
The Bridal Mask - super intense, there is action...but I think it's main thing is being intense and really, really good
Empress Ki - something is always happening, and definitely a really emotional story (it's 51 episodes though, but SO WORTH IT).
Dramas I've completed that I feel fit with your criteria:
The Princess' Man - never a dull moment, and just SUPER AMAZING and well done
That Winter, The Wind Blows - my absolute FAVORITE melodrama, definitely emotional. If you liked the main guy (Jo In Sung) in It's Okay, That's Love...you'll also love him here.
Signal - it's a total psychological endeavor ....it's SUPER well written and probably my most favorite drama I've seen so far
Marriage Contract - a really good melodrama that really hits your heart in the right places
Splash Splash LOVE - it's a 2 episode special, but totally worth it--super endearing.
The Master's Sun - a really good classic
Scent of a Woman - a really good melodrama
I Hear Your Voice - if you want to try a noona romance, this is the best one out there
City Hunter - a revenge-esque and romantic story. Probably Lee Min Ho's best work.
Secret - a really wonderful melodrama