I'm planning my wedding and I'm feeling stupidly sappy, so I'm in the mood for a good romance. There are a few things that I am absolutely NOT looking for:

- Love triangles.
- Noona romance.
- I like-you-I-don't-like-you-I-like-you.
- Series that start out with a lead hating/disliking their love interest.
- Forbidden romance.

I just wanna sink my teeth into a solid, mature (in tone, not age), realistic drama. Romcoms would be great, but any other genre will do just fine. Does anyone have any recommendations?
Queen In Hyun's Man - None of the above qualities that you mentioned. The lead-guy is super nice and also intelligent and there are sooo many cute and sweet moments between the couple. The first episode is a little confusing, but once you get past that, everything makes more sense. 

Healer - An amazingly well constructed drama. None of the above mentioned qualities. It's also super interesting/addicting and Ji Chang Wook is amazing in it. 

Hmm it's so hard because the minority of K-Drama are those. I recommend you : 
Healer (HIGHLY RECOMMEND), One More Happy Ending, Pinocchio, Reply 1997-1994-1988 (HIGHLY RECOMMEND), Kill Me Heal Me, Birth of a Beauty, City Hunter, High School - Love On, The Girl Who Sees Scents, The Producers.

And these are my favorites K-Drama, it may contain Love triangles, I like-you-I-don't-like-you-I-like-you, Series that start out with a lead hating/disliking their love interest & Forbidden romance, but it so good it's so worth it, you'll love it trust me just try it! Some are like heavy serious drama with comedy in it, and some just a simple Rom - Com.

- Master's Sun
- You Who Came from the Stars
- Secret Garden 
- Falling for Innocence
- Marriage Not Dating
- Fated to Love You
- Cunning Single Lady
- A Gentleman's Dignity
- My Girlfriend is a Gumiho
- Bride of the Century
- My Princess
+1 Healer, Fated to love you.

Also In the mood for love / 2046.  Romantic tension so thick you can cut with knife.  

But if you want realism paired with the best writing, dialogue, and narration (Waugh O.O) imaginable look to England: Brideshead Revisited (Jeremy Irons, Laurence Olivier, John Gielgud version).  Geoffrey Burgon's Ost is gorgeous - https://www.youtube.com/watch?v=Igmm-446qSk

Also Poldark (old one).
How many episodes do you want to watch?
@oyaji Hahahaha that was something!
Oh my Venus .. romance is sweet. No annoying second leads, no push pull, no horrible in-law's trying to break them up
Heart to Heart is one of my favorite mature dramas. It deals with social/mental illnesses. The male lead is kinda rude in the beginning but you can see that it is for the female leads own good. The twist towards the ending is a little cliche but the drama to me is very cute and romantic. 

It's okay that's love is another drama to try out for maturity  the annoying second lead doesn't last long is this drama 

Also if you enjoy Taiwanese dramas I suggest Bromance or Boss & Me there are annoying second leads but Taiwan writer's know how to pump up the romance/cheesiness to combat any negativity around the lead couple.
Can we get married? Master's Sun, Kings 2 Hearts
"It's okay that's love" is about marriage, trust, prejudice, independent women (don't expect "Oppa" , I've my own money)