Love Costume, Period, and Historical dramas. I watch everything though. I am a fan of international art. Chinese, Korean, Japanese, French, UK...Etc. My current favorite is Chinese epic dramas.
Favorite Chinese dramas: The Untamed, Nirvana in Fire, The Wolf, The Story of Ming Lan, Love and Redemption, The Joy of Life, Eternal Love, The Blood of Youth, and more :P. Some of my favorite "modern" ones are Hikaru No Go and The Youth Memories.
Favorite Korean dramas: Goblin aka Guardian: The Lonely and Great God, Moon Lovers: Scarlet Heart Ryeo, Mr. Sunshine, Mr. Queen., Under the Queen's Umbrella.
Favorite Japanese dramas/movies: Some classics: Pride (biased here, I was the translator of the series working with JTV), Long Vacation, Good Luck, and Orange Days. All of Rurouni Kenshin's live actions, and the anime. I'm also an anime fan, especially the classics like Evangelion.