I like ancient history, or I guess more appropriately history of societies that are only on the cusp of modernization. I don't even know why, but there is just something strangely poetic about that phase in the development of civilization, where society is only just crawling out of tribalism and the first hints of what will become the modern world is starting to appear. I guess it is sort of cliche, but the Greek and Roman worlds always seemed especially interesting. In both of those cases, that marriage between modern and tribal is especially apparent. 

But what time would I want to live? Now. I think the best times in history to be alive would be either the last 100 years in the Western World or the 2nd Century AD in the Roman world. I would imagine there is a Chinese equivalent, but I am woefully under-educated when it comes to China.