Your move, AFI.
The Korean Film Archive has started the Korean Classic Film Theater, a YouTube channel where in the past two weeks they've uploaded seventy classic Korean films from 1940 on that you can watch for free. Before you ask, yes, they have English subtitles on them!
The films are divided into 9 playlists that are grouped based on 6 decades and directors Kim Ki-young, Shin Sang-ok and Im Kwon-taek—three of South Korea's most renowned veteran filmmakers. This is a treasure trove given that many of these films are not available internationally, and many only in bootleg form. Plenty of them, especially ones made during or before the Korean War, are probably unknown to most.
The 80s and 90s playlists, however, contain more well-recognized films, including celebrated films like Hong Sang-soo's debut masterpiece The Day a Pig Fell into a Well, Park Kwang-soo's socio-political drama Black Republic, and Lee Myung-se's semi-autobiographical comedy Gagman. This is the period most commonly referred to as the Korean film industry's rebound period, right before it exploded into unprecedented international popularity with the turn of the millennium's Korean New Wave.
Out of the three filmmakers featured, Shin Sang-ok arguably has the most interesting career. The films on his playlist are all from 1961 and older, including his celebrated Prince Yeonsan, because in the 70s Shin became notorious as one of the many South Korean filmmakers kidnapped by Kim Jong-il to make movies for North Korea. Shin and his wife eventually escaped during a film festival in Vienna years later and sought asylum in the United States, where his career took a nosedive that eventually led to him directing his last film, the terrible sequel 3 Ninjas Knuckle Up.
The Kim Ki-young playlist doesn't include his most famous work, The Housemaid (1960 original, not to be confused with Im Sang-soo's 2010 remake), but it does have his breakthrough film Yangsan Province, as well as the other two films in his "Housemaid Trilogy," Woman of Fire and Woman of Fire 82, showcasing Kim's usual penchant for femme fatale characters and an exploration of surrealistic sexual perversion. Similarly, the Im Kwon-taek playlist is unfortunately missing Mandala, but has his award-winning film Sopyonje.
You can view all these films and more here.