The naked mole-rat lives for thirty years - compared to 1-2 years for other rodents - and we've never found any evidence that it can get cancer. Now we're peeking inside its genome to figure out what makes it special.
This particular rodent is the only known mammal species to possess negligible senescence, which means that it doesn't experience any decline in physical or mental faculties due to aging. Tortoises are probably the most famous examples of this, as they've been known to live as much as 250 years. (You can learn more about negligible senescence in this post.)