Calibanus hookerii. See more pictures of cacti.
It is a tough plant. Having been bred to endure dry air and drought, it will survive for years in less than ideal conditions. However, it cannot cope too well with humid air, overwatering and too much fertilizer. It can stay in the same pot for a number of years since it prefers to be a bit rootbound. To keep it in shape, give it benign neglect.
Caring for your cactus: