Elves live the longest (unless you kill them)
The human races are very similar to us (around 78-90 year lifespan more depending on their life)
Edit: Apparently Dark Elves can life for up to 1000 years most don't make it they generally live to the age of 800-900?
I don't think Dunmer live that long on average. An http://www.uesp.net/wiki/Morrowind:Interview_with_a_Dark_Elf with a Dunmer implies that they live around 150-200 years, while "purer" dunmer can live 300+(Benezia for example).
Mages live longer than others, if I remember correctly and that might be some of the reason of the Altmers long lifespan since they are very gifted magicians.
Bosmer probably have similar lifespans to the Dunmer.
All Elven races may have the potential to live for 1000 years, but this is probably tied closely to the respective traits in the families.
Nord, Imperial and Redguard live 70-90 years I think, but Bretons may live longer since they have both Nedic and Aldmeri ancestry.
Orcs may have similar lifespan to the human races, even if they are elves.
I have no idea how long Argonians and Khajiit live.