I picked 20th Century as I wasnt alive for the 60's or 80's and would love to be there growing up- despite the Cold War etc. I will be alive 50 years in the future (hopefully). Other wise time of Jesus or something.
Actually, on 2nd thoughts, I'd like to go back to the creation of the universe, and then to the creation of earth. I'd then set up a really long lasting timelapse camera. Go back to the present. Get it, and then piss creationists off by showing them it at every possible opportunity.
I would hurry up and go get a Mickey Mantle baseball card and hide it in my grandma's floor, then I'd come back to now, and tear up my grandma's floor, take that card, sell the shit out of it, and then buy my grandma a new floor. ....
I already know whats happened in the past, so I would go 50+ years into the future just to see what happens.