Just sharing my favorites (and also thinking it's the best ever made drama) which is: My Mister
That being said, there are many more of my favorites that I love so much, all 9.5 or 10s for me.
Someday or One Day, Flower of Evil, Misty and Youth of May, Cruel City and some more....
If you wanted Jdrama, there are some masterpiece there too, It's just J-Dramas aren't made with very high budget so the cinematography isn't up par. OST wise, they use much less music and aren't getting the popularity as the recent years's K-Drama, but the older J-Dramas are still much more known than older K-Dramas in contrast, so I'll only recommend older ones to get you into a different world of awesomeness.
Lipstick (1998) , LIFE (2007), Ice World (1999), GTO (1999), Liar Game (2007-2009),
Kimi no Te ga Sasayaite Iru (1997), One Million Stars Falling from the Sky (2002),
At least 15 years and some passed, yet these hold their own to the solid dramas from the recent days: