It appears that naked mole rats don’t age: every normal population of living creatures dies exponentially more/faster with age— that’s called Gompertz law. But naked mole rats don’t: their likelihood to die remains constant with age. And they don’t get cancer (well, hardly)!
Here is the article from Science Magazine:
I am sure they will eventually find out that, if they get old enough, naked mole rats eventually start dying off. But, given their size (size seems to life duration: small creatures don’t last long), at the very least they live astonishingly long lives!