Okay, I've been on a hiatus this year, and up until this week I had only watched 2 non-airing Korean dramas, time to change that.

Has to be Korean, has to be 16-24 episodes, has to be done airing, and has to be somewhat recent, because I can't watch non-HD dramas, it hurts my eyes (2006-2008+ dramas should be good).

I love dramas from every genre, so it doesn't really matter what the genre is. Except school/teen dramas, I want to stay away from that crap.

Please check my list before recommending, I've seen a lot of stuff.
From this year, I recommend It's Okay, That's Love, it finished airing just last week and was pretty good :)
There was also Marriage, not Dating if you like comedies, definitely my favorite this year (since comedy is my fave genre :3).
And as for rom-coms, Witch's Romance was really sweet and entertaining, definitely worth checking it out.

Anything from before 2014? I didn't watch those because they didn't seem particularly interesting to me :/
I recommend "Secret Love Affair" 
I'll try to list different genres:

Can We Love? - a drama about the lives of three women, involves romance and towards the end melo, personally I loved the tone of the drama
King's Daughter Soo Baek Hyang - a really good historical drama, might be a bit slow-paced for some but is solid from start to finish
Inspiring Generation - an action period drama, has writing flaws (especially after the writer changed around ep 10) but it's entertaining with great supporting characters
Secret Love Affair - noona romance with a large age gap, pretty mature atmosphere and great music (if you like this I'd also recommend A Wife's Credentials made by the same team and with the same lead actress)

And since you asked for dramas from before 2014, I'd also recommend Special Affairs Team Ten 2 from last year.

Hope you can find something to your taste among these^^
King's Daughter Soo Baek Hyang actually sounds interesting, I have considered watching it before, but the number of episodes does not please me too much... I'll have to think about it >:
True it has a lot of episodes, but since they're only 30 minutes long it feels like you're progressing pretty fast while watching. Well ~50 hours is still a long time to spend on a drama, but it's not as much as the ep count makes it seem^^