If only I can pick one...but, I can't. I would love to live during the '60s or '70s because I love the music of the period (Beatles, Jimi Hendrix, Led Zeppelin, Janis Joplin, The Doors, etc. ) and it's as simple as that.
I could also imagine myself living in England during the reign of King Henry VIII. The six wives were simply fascinating (especially Katherine of Aragon, Anne Boleyn and Anne of Cleves). Now that I'm going the historical route, I wouldn't also mind living in France during the time of Madame Pompadour or Marie Antoinette (probably because of the fancy dresses).
As much as these time periods sound so cool, I'm contented with the time period I'm living, thank you very much. (I can't imagine myself without an iPod and a really good pair of headphones)