Some of my favorites:
Korean
Splash Splash Love - short series. Student falls back in time to some pre-industrial era.
Scarlet Heart Ryeo - I'm sure others can speak of this show. I thought it was alright (better than the Chinese version).
Faith - doctor is taken to the past by a warrior to heal an injured queen.
Japanese
Nobunaga Concerto - I recommend this. Funny, I love the soundtrack and I love the actress who plays Nobunaga's wife. Basically a student without much luck travels to the past and becomes Nobunaga - the heir to a clan during the 'warring states' period (think of a civil war where different groups fight for power/control of the country). You can imagine he doesn't fit in with the bloody, warring culture of the times.
Chinese/Taiwanese
Back to 1989 - man travels back in time to a year or so before he is born (1989, Taiwan).
Shuttle Love Millennium - identical looking men swap places - 1936 and 2016 Shanghai( is the city I think?). They swap places multiple times throughout the show.
Go Princess Go - Be warned: there is a gender swap theme in it but the whole show is hilarious and I feel it deserves even more praise/recognition.
