You can thank this question for being the reason that I am on these forums today. I was looking for the answer to this question when I decided to look on the official forums, then found a whole forum section dedicated to Lore and fangirled all night long.
Anyway, what I found was that that is a very hard question to answer. There is no official lifespan mentioned.
One source, for example, claims that Dunmer live around 130 years, although Divath Fyr is around 4000 and other Telvanni are of similarly old age. Barenziah was around 300 during the events of the Tribunal expansion of Morrowind.
Uriel Septim VII was 87 when he was assassinated, and he looked fairly old, so I'd assume most of the human races live to be about 100, if not older. Bretons might live a little longer due to their natural magickal aptitude.
I remember someone in TESA: Redguard mentioned that elves live longer, whether he meant longer than all men or just Redguards, I'm not sure.
It's also a pretty popular opinion that Orcs live the shortest of all the races, around 60. I do not know why that is though, so I'm sure someone else could fill in the blanks.