Personally I love these wacky Chinese romance series like Go Princess Go, Oh My Emperor! and Cinderella Chef.
But if you prefer less romance and/or a story about people adapting to the ancient world with modern life knowledge/tricks:
A Step into the Past (Chinese time travel crime series available on Viki )
Man Comes to Tang Dynasty (Chinese comedy available on Viki)
Wan Neng Library ( Chinese time travel comedy that Youku put on Youtube)
Jin 1 and Jin 2 (J-drama series about a brain surgeon traveling to ancient Japan)
Live Up to Your Name ( medical k-drama about a doctor from Joseon dynasty living in modern times)
A Chef of Nobunaga (J-drama about a modern day chef who travels back in time ) and the sequel
Nobunaga Concerto (J-drama about a high school student who becomes a young warlord) and the movie