Naked mole rat
It must be difficult to maintain a vibrant self-image if you're a bald rodent, but it's not an issue for the naked mole rat. These animals live underground in insect-like colonies, and they have little need for good eyesight. Their hairless bodies are also an adaptation for their underground environment.
The San Diego Zoo points out that naked mole rats are more closely related to porcupines, chinchillas and guinea pigs than they are to moles or rats. They actually do have some hair: about 100 fine hairs on their body that act like whiskers to help them feel what's around them and hairs between their toes to help them move soil behind them when they are making tunnels.
Interestingly, naked mole rats are also among the longest living of all rodents given their size (they can live for nearly 30 years), and they have a remarkable resistance to cancer.