Mayan civilization in Sth America.
Times of the Roman Empire in Rome.
Times of the Pharaohs in Egypt.
The Dark ages. With all that wonderful advancements in science, art, medicine, astrology and all that happening in the muslim world.
And I'd love to have been in my 20s in the mid to late 60's/early 70s. I want that handlebar mostache, those tight pants, and a 69 Mustang!
I'd really love to be in all of those lost civilizations... to see how they lived and what technologies and 'ilms' they had.