It's recommended that we get an 8 hours of sleep a night. While we're sleeping, hormones help fix damaged tissue in the body, including skin. Without enough sleep, the body makes more stress hormones. This negatively affects not only the mood but also the skin, so a good night's sleep really is beauty sleep.
Stress and lack of sleep feed boost each other. When you're stressed, you tend to find it harder to sleep properly, and when you don't sleep enough, your body releases more stress hormones, which means you don't sleep. Insomnia caused by stress also puts you at greater risk for depression and anxiety disorders. Scientists are still trying to decipher how sleep (or lack of it) effects our emotions, but it seems that the emotional centers of the brain connected to depression and negative emotion run wild when we're tired.
Finally, the immune system just works better when you're sleeping well, making you healthier and more likely to be looking and feeling in top form.