In Deathly Hallows, Chapter 16, Godric's Hollow we are given the birth and death dates of James and Lily Potter when Harry visits their graves.
"James Potter, born 27 March 1960, died 31 October 1981"
"Lily Potter, born 30 January 1960, died 31 October 1981" (Pg. 268, British Edition)
This would mean that James and Lily were 21 when they died. I assume that Sirius, Lupin and Snape are all the same age. Lily and James would have been 17 when they left school in 1977 and would have had Harry when they were about 20 (approx. 3 years after leaving Hogwarts). Harry goes to Hogwarts in 1991 at the age of 11 (assuming he is born in 1980). This means that Sirius, Lupin and Snape would all be 31 when Harry starts school.
As for Dumbledore, he does have some living contemporaries. Several come to mind, whom we meet in Deathly Hallows. Elphias Doge writes an obituary for Dumbledore after he has died (Deathly Hallows, pg 21-24, British Ed.) in which he reveals that he attended Hogwarts at the same time as Dumbledore. Bathilda Bagshot (author of A History of Magic) also lived in Godric's Hollow and remembers Dumbledore as a boy (presumably she is older than him). Ron's aunt Muriel also seems to know a lot about Dumbledore, and clearly knows Elphias Doge (Deathly Hallows, pg. 128, British Ed.). She is also fond of telling people she's 107. I assume Dumbledore and Elphias are around the same age.
As for the other professors, I have no idea how old are they are, but I assume most of them to be somewhere between Snape's age and Dumbledore's.
Hope that helps!
+1 for taking the time to give an actual answer