I second this BUT, I would move it from the 60’s to 1965-1975, just for the music…that way you get the The Beatles and Hendriz as well as the Stones kicking ass, Zappa, Zepplin, The Who, The Doors, The Dead…I am not sure of I’d want to live in L.A, New York or San Fran though.
The war in 'Nam would troubles me, but the war on Iraq also troubles me so that is a wash I guess. Oh, I am 27 if that makes a difference to you at all.
Late 18[sup]th[/sup] Century. Massachusetts. You will find me perforating Redcoats at Concord…
I dunno…I’m pretty happy in the time I live in.*
If, for no other reason, then the fact that I might be crippled and/or insane if I were born in the past. 200 years ago, I’d be dead. How 'bout you?
Ranchoth
*(Though the future might be best…especially when Holodecks both technically possible, and cheap to operate.)
If I were Middle Class or Upper Middle class, I would prefer the periods of economic prosperity under the rising tide theory of economics:
The Dutch Republic 1560-1700, (even if I had to wear those big frilly ruffs)
Spain under Phillip II
France under Louis XIV (Even more frilly clothes)
Elizabethan England (but I don’t look good in tights)
Europe between the Franco-Prussian war and WWI.
But the 1960’s? Let me tell you, not if you were a draft eligible male. You can’t believe the pressure that 2,000 lb. gorilla placed on your life. Also the Civil rights and anti-war protests, combined with the assassinations of 1968 appeared to irrevokably sundering society.
The Titanic may have been going down, but the band sure was good.
I’d pick Swinging London in the 1960s, but only if I could be about 70 lbs lighter so I could look like Twiggy. 
I’d like to live in the late 40s, early 50s, if I were single. I just love the way women looked in that time period. 
As far as the coolest time to experience, I’d love to live in 1780s Vienna. Ahhh…the music!
Jman
Regency England: As I’ve read too much Austen and I look good in a shift
Victorian India: I like the idea of being a spoiled Memsahib. Scandalizing the other European women by wearing a sari and gossiping with my ayah.
Late 19th early 20thC Ireland: I’d like to see, first hand, the political changes in the country.
I think my two favorite historical periods are the Renaissance and the American 1940s. Going back in time to live there… I dunno. I’m awfully addicted to comfort and convenience, so unlike others have said, I would prefer to go back WITHOUT knowledge of the future. Yeah, I’d miss out on some stock opportunities, but at least I wouldn’t know I was also missing out on antibiotics and central air conditioning.
Here and now. Things get better, not worse.
Provided that some sort of lifesaving immunization protocol could be worked out, I’ll take a big leap into the unknown and try for 3004 (be it Utopia or Dystopia, or something in-between), because I have a ton of questions:
How have world civilizations come to terms with demographic pressures vs. ecological constraints? Did humanity manage to preserve our current (ailing) variety in ecosystems? Were all the oceans ruthlessly overfished? Did the world’s coral reefs die out? Is there a dominant or (economically/politically/culturally) unifying language, and by any chance is it still English? Which languages were lost? And ethnicities? Any new ones (of either)? How comprehensible are my English and subfluent Spanish? How did the current geopolitical alignments work out? How has the United States fared? How many of the world’s nations are peaceful, stable democracies? Are there still dictators? Is Europe still unified – and better than ever? Is there a unitary world government? When did the petroleum finally run out, and how did the most-developed nations in particular cope? Was there ever a global WWIII? Was it nuclear, and if so, was it sparked by a madman dictator, a mechanical breakdown, a misinterpreted flock of geese, or what? Was it fought along religious lines? What was the extent of the destruction, and how long did it take humanity to substantially recover? Is bellicose and intolerant religiosity still a source of political and cultural conflict? Have humans managed to further cultural evolution to the point where no cultures could be said to be structurally sexist, racist, etc.? Have the Jewish people managed to maintain their ancient identity for yet another millenium; does Israel still exist, and does anti-Semitism still persist as a crude ideology of sorts? Did the polar icecaps finally melt, and have they ever returned? Did we manage to avoid any globally-catastrophic asteroid/meteor/comet impacts? What diseases continue to ravage the species? Have we co-evolved with HIV and its descendants to achieve a degree of commensualism or something? Did we reach Alpha Centauri yet? Any contact with intelligent extraterrestrials? How sad, and much fun would it be to study the history of global pop culture, tracing the eventual loss of most of our current pop ephemera, but sampling the innumerable trends and innovations (one hopes) to come? Which albums, movies, etc. from the 20th-C. survive in archived form in 3004, and how radically different have entertainment, the arts, and sports become? Are football, baseball, basketball, golf, etc. still popular? Do they still hold the Olympics, and what are some of the current world records? What do people do for fun these days? To what extent is random violent crime still a hazard? Was crime largely stamped out by various privacy-eroding measures? If modern civilization has managed to survive, are people’s lives even more harried, stressed-out and complex than they are now? How psychologically healthy, and how happy, are most people now? How useful would I be as an eyewitness from my own time in correcting the historical record and filling in the gaps?