Unless you want English ones, in which case I highly recommend Supernatural, Once Upon a Time, Grimm, The Walking Dead, Vampire Diaries and Teen Wolf!
Okay. Now I'm done. :)

OHMYGOD, SERIOUSLY. This may be late (*sobs* I've been internet deprived for almost a month!! DX) but I can TOTALLY help you out with this!!! XDD
Lie to Me = all sorts of adorbs. X) Just, seriously, I can't explain it, just watch it, you won't regret it. ^^
City Hunter = Action, killer adorbs Lee Min Ho, killer adorbs story in general, bad-a** action scenes, fighting and just about everything you can imagine. It's my absolute favorite. X) Plus, one of the main dudes looks so much like Donghae, my friend (whose bias is Hae) just called him Donghae the entire time. ^^
Personal Taste = Really funny and cute. ^^ Another Lee Min Ho one. ^^ I haven't actually finished it. I still need to watch the last, like, two episodes. >.< It's super good, though. :)
My Princess = also completely adorable. Plus, the main character is another Hae look-alike. :)
Boys Over Flowers = probably one of the most-watched dramas. It has Lee Min Ho (In case it's not obvious, I completely love this man.) and Kim Hyun Joong from SS501 and a dude from T-Max (I can't remember his name, though. >.<)It was one of my first dramas, and I still love it. X) Like, 25 episodes long though!
Heartstrings = REALLY freaking cute. Like, really. Yonghwa is in it! (from CNBlue. LOVE him. XD)
You're Beautiful = It's probably my second favorite. Jang Geun Suk, Yonghwa AND Hongki (from FT Island!) as the three main characters, plus Park Shin Hye (probably my favorite female actress) is the MAIN main character. :) Anyway, it's really good, too. ^^
I also recommend Cinderella's Stepsister (but it's pretty sad) and That Winter the Wind Blows/Wind Blows at Winter/ whatever else it is called. I honestly only watched those due to the fact that Sungie sang the OST. X)) But I REALLY love Wind Blows at Winter. Like, seriously. Cinderella's Stepsister was really good, too, just sad. :/ I still love it, though. ^^
There's more, but I think that should keep you busy. I'll stop now with this epic long comment. ^^;

Not really* supernatural

Vampire prosecutor rocks.
There is season 1 & season 2.
Just watch! It's really good!!

Arang and the Magistrate is very cute too!!
It's about a ghost and a magistrate.. hahah don't tell you much or it will spoil the suspense..

Although this is not a Korean drama,
But the Japanese drama 'Galileo '
is one show that I always recommend people to watch if you like police and procedure type of dramas adding with a dash of 'supernatural ' ...
Actually not rest supernatural...
It's on a rookie policewoman seeking help from an unwilling genius Physics professor to solve cases.

There is 2 seasons for 'Galileo'...
Currently I am watching the last few epis of it... but I have to admit..
Season 2 is not as great as season 1..

Smile, You is quite a long drama with 45epis..
The story can be alittle draggy in the middle.. but overall I find that it's an Ok show to watch.. because some parts is really funny!!

yeah.. that's all for now..

I just finished watching Vampire Prosecutor and i love it so much.
It's like those csi series in which they solve murders, but one of the investigators is a vampire who can see what happened to the victim by drinking their blood :p

You need to watch reply 1997. period.

Drama/Adventure:
City Hunter (Probably one of the best dramas I've seen that has a good mix of comedy, romance, action, drama, and melodrama. If you like City Hunter, you may like 'Faith' as well since Lee Minho's in it and it has a slight similar feel to it.)

I Hear Your Voice (Has an outstanding Noona-Dongsaeng relationship that's being fleshed out quite well. Plus, it's a good mix of drama, romance, and suspense. Well picked out cast and the crime aspect is easy to understand and follow.)

King 2 Hearts (Funny, romantic, drama, and just something that's good to watch whenever. The chemistry between the leads is great and even supporting characters are fleshed out well.)

High School/Kpop:
Dream High (It took me a bit to get into it as stuff like this isn't my thing, but after the first episode, it was executed well and IU's character is so cute.)

Monstar (Has similar feeling to Dream High, but picks up a bit quicker than DH did. Good overall cast and has a wonderful soundtrack. Long episodes, but very engaging for the most part.)

However, due to what you have watched so far, I suggest going with Shut Up! Flower Boy Band, School 2013, King 2 Hearts, Dream High, Reply 1997, or City Hunter first, especially if you're more into dramas that have idols as actors or kpop is a slight theme to them.

Bromance:
Shut Up! Flower Boy Band(Great actors, great soundtrack, makes you cry barely an episode in, but very uplifting, bromanc-y and more about the friendship than romance as the series progresses. A must watch, really.)

School 2013 (Bromance galore, especially angsty, tear jerking, awesome bromance that starts with stabbing you in the heart and turns into awesomesauce as the series progresses. Lots of heart and more focus on life long friendships rather than romance.)

Tumbling (J-drama, but it has Seto Koji and Yamamato Yusuke in it. Very friendship based, but has some good uplifting themes involved. Actually, watch any drama with Yamamato Yusuke and Seto Koji in it, because these two are wonderful actors.)

Bachelor's Vegetable Store (Full of bromance and some very sweet romance as well.)

Historical:
Bridal Mask (Long, but well thought out and pretty daring if I must say so.)

Romance:
Operation Proposal (Lots of cute scenes and can drag on a bit, but Yoo Seungho's in it and his chemistry with the other lead is great.)

Comedy:
Protect the Boss (Jaejoong's in it, but overall, it's a funny comedy that keeps you laughing for the most part. Last two episodes are jusst decent, but overall it's a good series.)

Skip Beat (Taiwanese drama, but Siwon and Donghae are in it, and it's pretty cute and funny.)

Reply 1997 (More RomCom, but it's one of the breakouts of 2012 dramas, along with Shut Up! Flower Boy Band.)

school 2013, because since we like fanfics, you may enjoy the bromance keke
i also think the thousadth man (with t-ara's hyomin) is quite funny
and is not because i'm a sone (since i didnt like fashion king), but i think love rain (with yoona) and the 3rd hospital & the currently drama cyrano agency (with sooyoung) are great
also, i like Cheongdam-dong Alice, is cute XD

Try oldschool dramas like Autumn in My Heart, Beautiful Days and then My Girl and Princess Hours ^^

"Dream High" is really good and has a bunch of JYP stars
Um, "You're Beautiful" is awesome bc it has Hongki (ftisland) and Yonghwa (cn blue)
But for the best angsty/dramatic/amazing/feel inducing drama I would recommend "May Queen" this is prob one of the most frustrating to watch but it's good bc u really connect with the characters. It's def one of my faves ^^

Oh, try My Lovely Sam Soon.
I watched it last month and loovvvveee it.
Oh and have you even seen Full House.(The one starring Rain)

i wanna watch siwon's drama "The King of Dramas"
it seems really funny,siwon's character(kang hyeonmin) is completely different from our wonnie in real life - he's arrogant,conceited,self-centered etc. and really funny xD
so if you watch that,please tell me if it's good and worth watching 'cos i'm planning to watch it when i find time ^^
oh and i wanna watch miss panda and hedgehod...what's it like?

president ft sungmin is great, 20 episodes and has you going through emotions like crazy, I want a second season but that wont happen, but I love it, best drama out there.

You should try Flower Boy Next Door, You're Beautiful, or Operation Proposal :)