In Korea, those dramas are usually referred to as sageuk which.. doesn't mean anything else in fact.
Giving examples? Well, let's just start with Secret Investigation Record which is not a typical sageuk drama (since it's somehow mixed up with the X-Files). We have for other examples Queen Insoo (starring Baek Sung-hyun, guess who'll watch this?), Chuno, Deep Rooted Tree, Yi San, Jumong, Gu Family Book, The Moon That Embraces The Sun, Faith and many many many more. Those are just a few examples, and the list probably could go on forever. Oh, and I almost forgot about Jang Ok Jung, Empress Ki and Jung Yi, Goddess of Fire. As you might notice, there are dozens and even more sageuk dramas.
Why do K-fans watch those dramas? We study history!
As to why that many historical dramas are filmed.. I have no idea. Even after doing some research I still don't really understand the reasons but maybe I will find out about that someday.