And why... if you can you be bothered explaining ahahah ~

Of any genre, from any country.

Full House (Thai)                                    Really good romance drama
W (Korean)                                             Very good filled with suspense and fantasy
My Girlfriend is a Gumiho (Korean)       Again fantasy, at some points really funny.

In looking through your list, here's what I'd recommend:

Age of Youth - Charming nostalgia of friendships, love, and life. It's impeccably written with extremely likable characters and I always found myself wanting to watch the next episode. It's simply BEAUTIFUL.

Dear My Friends - Again with friendships, but it goes into life lessons and the meaning we place on 'time.' Also, if you are a fan of romance, it has my all-time favorite couple in it as well with the Jo In Sung character.

The Princess' Man - An epic, revenge-filled, Romeo & Juliet, fast-paced sageuk. It's incredibly addicting, I absolutely ADORE it.
49 Days (K-drama)                   Unique fantasy drama!! 
Ryusei No Kizuna (J-drama)    A family mystery drama which is surprisingly funny as well!
White Christmas (K-drama)      A unique psychological mystery drama...loved it!!
Probably 3 dramas that are in different genres so you have a little variety. However, I somehow ended up choosing dramas that have an element of suspense/where certain things are not revealed until the very end. The genres are still pretty different though and the type of suspense is a little different too.

W - fantasy, romance: lovely relationship the main characters, filled with cliffhangers and unexpected turns - i couldn't wait for a new episode to come out.
Age of Youth - life, friendship, university setting: great characters, heavily focused on characters & their backgrounds rather than 1 plot, good music too.
I Remember You - crime, investigation, psychological: very interesting characters, you don't know who is who and what everyone is capable of for quite some time, MDL has classified this as romance, but it isn't - not in my opinion anyway. 
I would recc any of my favourites, because I believe in my mind that they are the best. But clearly, everyone has different tastes! If I had to just pick 3 in general I would go for:

The Village: Achiara's Secret:
I think everyone should get a taste of this plot! It's still vivid in my mind. I enjoyed every moment while this drama aired. I really enjoy mystery/thrillers and this one really made me happy last year. [Other similar ones I usually think of include: God's Gift, Signal, and Two Weeks.]

Age of Youth: If you enjoy those slice of life dramas that really feel more like reality than a drama with a million cameras in the back, this is something you should check out. I didn't think I would enjoy it as much as I did, but I did! The director and writer really knew what they were doing. I loved getting insight on all the different characters and their lives. And I like when dramas do special things that are unique to that drama (like the interview tidbits at the end of this one.) [Others I think of include: Heard It Through the Grapevine, Misaeng (Incomplete Life), and Unkind Women.]

Orange Days: This one is Japanese. My Japanese list is very limited, but this drama always comes to mind when someone mentions Japanese drama. I thoroughly enjoyed this, I've always enjoyed dramas with life obstacles (like disabilities) and in this drama the main character is deaf and uses sign language to communicate (I find that very fascinating. *If anyone knows other dramas that use sign language please let me know!*) [Other dramas that come to mind: Silence (Taiwanese); main character goes mute. It's been years so my memory is a bit fuzzy, but I remember I liked this and I still remember bits and pieces. A drama you can't forget is a drama worth watching! at least in my opinion!]

Bonus: If you're ever looking for a light drama with comedy and romance (the cute kind and not the ones that trick you with their tags and end up being a freaking trainwreck and 99% melo) look no further than the currently airing Shopping King Louis. PS: it can get a little sad at times, but it's worth it.
Moon Lovers: Scarlet Heart Ryeo
Mirror of the Witch
The Master's Sun

Simply because I'm extremely picky when it comes to watching anything but I was hooked on these from the first episode. 
W: http://mydramalist.com/16589-w You just need to see this. Everyone needs to see this. 
It's Okay, That's Love: http://mydramalist.com/9289-its-okay-thats-love Good chemistry between leads and amazing plot!! Definitely worthwhile if you're willing to have a few (okay many) heart-wrenching moments!
Love O2O: http://mydramalist.com/15031-love-o2o Irritated with those drama relationships that are about as strong as dandelions in a windy field? Watch this one to see the one of the most satisfying romances! BONUS: WANG WANG!!!
1. Age of Youth- Heartwarming friendship story and reflections of reality. This show offers you the lessons in life and characters which you can relate to so much to yourself. I would like to reward this show for its best character development.
2. Cruel City- Thrilling and heartwrenching. Gives you a rollercoaster of emotions and it has the most unique characters where you can't read them like a book. It has a fair amount of twists which keeps it fast-paced and addicting.
3. Kill Me, Heal Me- Calm and relaxing medical drama. This one soothes your mind with the vast amount of humour and will also break your heart. To say that Ji Sung's acting is amazing would be an understatement.