Syllogistically speaking, Socrates didn't die of natural causes, therefore the Greeks had lifespans the same as ours. Or something.
But there's no doubt that Romans, Egyptians, and Greeks were dropping dead at age 30, 40, 50 and 60 -- at much higher age-specific mortality rates than today. Estimating the overall age profile is difficult and requires models.
Fortunately, there has been a study of the length of life in ancient Greece, that shows, that Socrates was not a unique case:
In a study of all men of renown, living in the 5th and 4th century in Greece, we identified 83 whose date of birth and death have been recorded with certainty. Their mean +/- SD and median lengths of life were found to be 71.3+/-13.4 and 70 years, respectively.
Of course, the lifespan of "men of renown" should be correlated with that of the general population, but with a higher mean, since men require time to achieve "renown". But, certainly the figure of 71 years does not seem too different from that of more recent men of renown, which is perhaps more surprising if one accounts for the high levels of violence in ancient Greece.
John also writes:
More important, we don't have a clue what the maximum lifespan may have been 200, 500, or 2000 years ago. Such a tiny fraction of people make it above age 100 today that we could hardly expect to find any of them at all from skeletal samples. Nor can we expect accurate ages from historical records -- Methuseleh, anyone?
We do have some fairly secure dates for at least some ancient individuals. Strabo died at 88. Sophocles died at 90. Democritus' life span was said to be anything from 90-109. Alexis, the comic poet reached the age of 100, Isocrates, 98. So, there were probably centenarians in ancient times, although what the maximum was is anyone's guess.
Psalm 90:10 gives the length of life as 70.
The days of our years are three score years and ten; and if by reason of strength they be fourscore years, yet is their strength labor and sorrow; for it is soon cut off, and we fly away.
Herodotus (1.32) has Solon give the "limit of life" at 70.
Croesus, you ask me about human affairs, and I know that the divine is entirely grudging and troublesome to us.  In a long span of time it is possible to see many things that you do not want to, and to suffer them, too. I set the limit of a man's life at seventy years;This suggests to me that a length of life of 70 was formulaic in the ancient Mediterranean, and corresponds quite well with the average recorded length for prominent Greeks.
Plato, in the Laws introduces a law that the guardians should rule from age 50 to at most the age of 70. Since the Laws is a work of political reform, we can assume that common Greek practice of the day (which is corroborated by historical knowledge about old-age statesmen) allowed for much older rulers, and, hence, such individuals existed in fairly substantial numbers -so that their rulership would become the object of a formal prohibition.
Aristotle, comments (in the History of Animals) that:In a famous passage of the Politics, after noting that male and female generation length is at most 50 and 70, he prescribes the ideal marriage age:
The reproductive function in men usually continues active till they are sixty years old; if they pass beyond this period, till they are seventy; and some men have had children at seventy years old.
Women should marry when they are about eighteen years of age, and men at seven and thirty.The prescription to marry at 37, suggests that early death must not have been too common; otherwise, it would be difficult to maintain the population's numbers, a topic which clearly occupied Aristotle, who commented on Sparta's oligandria in the same work.
Lucian's Macrobii is dedicated to the topic of long-lived men, after listing the ages of various ancient and semi-mythical people, gives the ages at death of several historical individuals, including some fairly reliable ones:
Of the orators, Gorgias, whom some call a sophist, lived to be one hundred and eight, and starved himself to death. They say that when he was asked the reason for his great age, sound in all his faculties, he replied that he had never accepted other peoples invitations to dinner!
Of the historians, Ctesibius died at the age of one hundred and four while taking a walk, according to Apollodorus in his Chronology.
UPDATE V (Aug 31)
Hieronymus, who went to war and stood much toil and many wounds, lived one hundred and four years, as Agatharchides says in the ninth book of his History of Asia; and he expresses his amazement at the man, because up to his last day he was still vigorous in his marital relations and in all his faculties, lacking none of the symptoms of health.
A reader writes in the comments:
The maximum life expectancy for humans seems to have been about 120years throughout recorded history.
"My Spirit will not strive with man forever, for he is indeed flesh; yet his days shall be one hundred and twenty years." Genesis 6:3
"From Cicero’s death to our day is a hundred and twenty years, one man’s life-time." Tacitus, "A Dialogue on Oratory", 17. Tacitus writes of seeing a 120 year old man in Britain in the 1st century A.D.
120 years as a length of exceptionally long-lived people is also mentioned by Herodotus:
The Icthyophagi then in their turn questioned the king concerning the term of life, and diet of his people, and were told that most of them lived to be a hundred and twenty years old, while some even went beyond that age- they ate boiled flesh, and had for their drink nothing but milk.
Of course we can't take the veracity of this story at face value, but the choice of number may suggest that it is as great as it could be without becoming unbelievable to the audience.