Sleep is an important part of life. If you don't rest you will wear out your body and mind. Take me for example. I am about a week late on this post because I was so sleep deprived, I destroyed my immune system and ended up with two serious inner ear infections, strep throat, and bronchitis. That was fun (Note the sarcasm).
Anyway, as far as your characters go (because I'm always involving them), sleep is just as important to break up the action that is constantly going on in your fictional world.
Try to imagine a world where your characters weren't allowed to sleep. This is pretty easy to do if you've ever missed a night of sleep (can anyone say kids!). Think about the way you feel after you've been awake for 20 some hours. You can't focus, you hallucinate. Those are just the immediate things.
The longer someone goes without sleep, the worse things get. Someone who has gone days without their fourty winks could become seriously ill to the point of their body failing them. Not good.
So, do yourself a favor when your writing. Give your characters a break, and take one yourself to get a good nights rest.