Mighty is a game with the 52 card pack (with one joker), that is said to be popular among students.
Hoola is a rummy game, in which seven cards are dealt to each player.
Hwa-tu is the Korean name for flower cards (similar to the Japanese Hanafuda). The most popular game played with them is Go-Stop. There is also an older game called Min hwa-tu, and maybe other games.
Golpae is the Korean name for Chinese dominoes - I am not sure what game is played with these in Korea.
In his book "Korean Games, with notes on the corresponding games of China and Japan" (published by the University of Pennsylvania, Philadelphia in 1895, and reprinted by Dover Publications in 1991), Stewart Culin describes various Korean games played at that time with Chinese dominoes, and others played with a type of long narrow cards characteristic of Korea. These Korean cards had ten-card suits, each consisting of numerals one to nine and a general. There were four, six or eight suits, making a pack of 40, 60 or 80 cards. I do not know whether any of these games have survived or whether cards of this type are still to be found.
The World Casino Directory includes listings of Casinos in South Korea and Casinos in North Korea.