Take an all time great, and stick him in a different era. How would they do? For arguments sake, assume their playing style would not change, but training/nutrition/etc would be the same as others in that era.
Laver: He played in his best era. At 5 foot 8 inches, I think he would be dominated physically in more modern times.
Sampras: Stick him in the late 60's, and he dominates 3 of the 4 Slams. All on grass with wood racquets would suit him quite well. He'd still never win RG though.
Borg: He was bjorn 30 years too soon. The courts and equipment of today would have been a perfect fit. We'd have 4 guys splitting the Slams instead of 3.
Federer: Born 10 years too late. The 90's would have been his best era. Faster hard courts, faster grass courts, and I don't believe he benefits from today's equipment as much as the other guys. He would have struggled a bit more on clay, but overall he'd come out ahead.
Nadal: Like Laver, I can't imagine him playing as well in any other era. Take away the poly, give him a smaller racquet, and stick him on faster courts - he would still have dominated clay, but he would struggle to win any other Slams.
McEnroe: Like Sampras, the 60's would have been his best era. With his touch, he might have even been more successful on clay than he was in his own era (I don't care what surface we're on, I don't want to try to pass him at net if I'm using a wood racquet).
Djokovic: Probably would have been a bit better in the 90's. The smaller racquets would have been just fine for his clean strokes, but any earlier and his serve/volley would have been a liability.
Connors: Like Djokovic, the 90's would have been his best time. A great fit for the dawn of the baseliner era, but he hit too flat for today.
Agassi: He played in his best era. Like Djokovic, any earlier and his serve/volley holds him back. Like Connors, his flatter strokes don't benefit from the new strings.
Overall, I think Federer is the most versatile and could have adapted well to almost any past era. However, I think the 2000's was the last era he could do well in, because I believe the 1 handed bh will not hold up over the next 10 years and beyond. On the other hand, just as I think Nadal would have been less successful in past eras, I believe his style is where the game is headed, so his best era might not have happened yet.