Humans / Worgen / Kul’Tirans: Propably like Humans on our World
Dranei and LF Draenei: Functionally immortal, as far as i know.
Gnomes: I think a near human lifespan
Undead: Functionally immortal as long as there are spare parts.
Goblins: As far as i know shortlived but breed fast. Consider them sentient rabbits.
Mag’Har and Orcs: Close to humans, we know Saurfang is around 70 and he is considered old. Drek’thar is older.
Pandaren: No real source, but i think close to humans, at max around 100 years.
Highmountain/Bloodhoof Tauren: again, close to Human life span
Dwarves: longer than Humans, i thing 200 years but i don’t really know.
Dark Iron Dwarves: same as dwarves, they are the same race.
Trolls: Most trolls don’t get old because they die a violent death. I think close to Humans when they are allowed to reach that age. But Loa play a role and special characters can get older when gifted by them.
Zandalari Trolls: same as trolls maybe a bit longer, Rastakhan was more than 200 years old, but he was gifted by Rezan
Night Elves: Functionally immortal
High Elves, Blood Elves, Void Elves: Same as High elves, again same race just imbued with Fel (mostly cleansed) or Void.
Nightborne Elves: Thalyssra lived during the War of the Ancients, so they propably are as immortal as Nightelves.