Bromance:
- A Gentleman's Dignity (I am shocked no one has mentioned this one yet since I feel like it's typically one of the first bromance dramas that come up in discussion and I thought it was very well done)

Self-Sacrifice:
- Ugly Alert (Yes it's long, but it definitely illustrates self-sacrifice and it is one of my all-time favorite dramas [I watched it twice] and I see it's on your PTW)

Noona Romance:
- What's Up Fox (I haven't actually seen this one yet, but I have heard people say that it's one of the best and most realistic noona romances)

Womance:
- The Woman Who Still Wants to Marry (I've only seen the first episode, but the friendships between the women are one of the main focuses of the show).

If I think of more later I'll add them.
1 Noble sacrifice / self sacrifice

>
Arang and the Magistrate (Kdrama)
>China Town (KMovie)
> God's Quiz (Kdrama)
>Healer 
> Hyde Jekyll Me
>I Hear your Voice
> Kill Me Heal Me
>Missing You
>My Girlfriend is a Gumiho
> A bittersweet life

Bromance

>School 2013
>I Remember You

3.Noona Romance

>
I hear your voice
> The Woman who still wants to marry
>Marry him if you dare


4 Sticky Situation

>A Bittersweet Life
>a love to kill
>Autumn's Concerto (T)
> China Town (Kmovie)
> Bad guys
>Blind (Kmovie)
> I saw the devil (Kmovie
>Healer
> Kill me Heal Me

can't think of others. theyre already suggested lol
@Wanderingjinny, thank you very much for your suggestions, added and yes if somethings else comes to  mind do tell :)
@Spring, added some of your suggestions as well, thanks!


I think I need to elaborate a bit better about sticky situation list because it seems things are getting a bit blurry and it's totally my fault. So sticky situation overload is when:

1. Through the series of events hero life sucks to the point where one starts to wonder where he will get a break, but the hero stoically endures while the viewer is worried whenever things will end well. 
2. Hero is dragged into many situations where he risks and endures great bodily or/and mental harm. Should happen many times not just once (every sageuk in existence seems to have one episode that involves being thrown to prison and tortured, I'm talking about more than a one time thing).
3. There is angst! Angst and manly tears are important. I'm a bit wary of melodramas because it easy to get to the point of things being ridiculous, so it is a fine balance here.
4. The hero is stoic, self-sacrificing, loyal to a fault type.

All of the above must happen. The whole point of such dramas for me is the quality of the hero, the obstacles he has to overcome and the way it is shown. The more i think about it the more I conclude that it's not so much about violence and gore, as it is about the angst and the mood.

For instance I saw the devil while very interesting movie does not qualify, because the main point of that movie is "who is the devil" and the protagonist is a very different type of hero. Healer is another excellent drama but while the hero posses the quality of the hero I'm looking for, the drama as a whole is rather light on points #1 and #2 and even #3 is more refined/subtle.

Two weeks qualify because in order for the hero to achieve his goal he is hunted, shot at, stabbed, all the while he agonize over the fact that he might not able to make it to his goal, which is to save his child.

East of Eden qualify because never mind all the beating the hero receives from random mafia guy, the hero's sole purpose in life is to help his family no matter the personal cost and he constantly pays.

Strangely Crazy for You while was suggested as noona romance also qualifies, because the hero does excellent job at torturing himself in almost every single episode, no need for bad guys.

Hidden Identity is a bit on the fence. There isn't that much angst and it's not so much the main cast that qualifies, but there is one supporting character who is the stoic, loyal type and it really sucks to be him in that drama. I'm still pondering if I'm going to keep it, but for now it's in.

Also, there are so many wonderful kdrama suggestions, but almost no jdrama or any other country drama, I wonder if its because the majority here watch mainly korean drama? Jdrama, cdrama, tdrama, etc. all are welcome.
I don't know if it will fit but, try White Christmas..
In Faith the main male lead has lots of self sacrificing, but it's kinda sporadic. 

Heirs has some good bromance, and Cheer Up (Sassy Go Go) has some good ones too!
Ouroboros and Cruel City have some bromance but its a bit... more dramatic... than feel good...

As for sticky situations: Oh My Ghost. She willingly gets possessed by a ghost... what could go wrong?
Ex Girlfriend Club, he has all of his ex-girlfriends meet, and they become good friends. (This one was cut short so idk if you want to add it)
Second Time Twenty Years Old- goes back to college at 40. It's interesting and messy but not really dramatically sticky.
Rooftop Prince - trying to survive in the future. 
Secret Garden - m/f body switching is about as complicated as it gets. 
Mask - the most melodramatic of the sticky situations I can think of, main lead takes place of rich doppleganger and gets married....
@Azzuritis - the bromance in Cruel City is actually one of my  favorite ones, added Ouroboros, thanks!

@Spring - not sure for which list you are nominating White Christmas?

the lists are filling up very  nicely, thanks again, everyone! And of course I'm always looking for more
1. Self-Sacrifice
Faith
Scholar Who Walks the Night
The Girl Who Sees Scents

2. Bromance
A Gentleman's Dignity

3. Noona Romance
I Hear Your Voice

4. Sticky Situation Overload
I Hear Your Voice
Yong Pal
I've seen way more J-dramas than K-dramas so I will focus on those for my part, while trying not to repeat what's already been suggested above. Also since J-dramas don't necessarily feature romance by default, some of these are primarily workplace dramas that happen to have a Noona romance element in them. Also, I wasn't sure what constitutes a large-enough age gap for your criteria so I tried to go with 5+ years, and/or if the heroine made note of the male lead being younger.

Noona Romance:
Anego
Bijo to Danshi (though no one's subbed it, sadly)
Love to Eros (a.k.a. Love and Eros)
Koishite Akuma (though I should note the heroine is the naive-type so...)
Nemureru Mori no Jyukujyo
Ohitorisama
Over Time
Papadol! (a.k.a. Papa wa Idol!)
Platonic
Sapuri (a.k.a. Suppli)
Satorare (somewhat...)
Second Virgin
Seijo
Shima Shima
Sore wa, Totsuzen, Arashi no you ni..
Starman ~Kono Hoshi no Koi~

And not in the MDL database: Toshishita no Otoko (a.k.a. Younger Men)

In ensemble casts:
One of the couples in Otona Joshi (a.k.a. Lady Girls)
One of the couples in Bitter Sugar
One of the couples in Ishitachi no Renai Jijou (a.k.a. Doctors' Affairs)
One of the couples in Tatakau! Shoten Girl

Movies:
Bashauma-san to Bigmouth (a.k.a. The Workhorse and the Big Mouth)
Tokyo Tower (the 2005 movie)
Don't Laugh at My Romance
Wood Job (kinda...)
Yuriko no Aroma

And a few Korean titles I don't think anyone's mentioned yet:
I Love Lee Tae Ri (a.k.a. I Love Italy)
Romance (the 2002 drama - though really the actors aren't that far apart in age, it's a teacher/student romance)
Rude Women
Venus Talk
(movie)
...and the Botox movie, if/when that ever comes out.
@AriaSaven,   thanks! I've added some :)

@kittyflumpin, thanks to you my noona list has become quite sizable! Some of the stories sound really fun, like the one with the murder suspect and lawyer.

About the age gap, i guess my main concern is that when it comes to noona romance at one hand I want to see the age gap, not just in appearance, but in how these people view romance at their respective age, the (potential) conflicts and worries or the lack of those (depending what the story is about) and on the other hand I don't want to see a story that tells its viewer that only awkward, inexperience and/or immature woman can have a relationship with a younger guy, I think that is my biggest turn-off