Sleep is one of the signs and blessings of Allah which is mentioned in the Qur'an.
Allah gave us sleep as a time of rest and recovery. Sleep makes us humble and reminds us that we are not invincible. Even if we are the most powerful person in the world, we still have to sleep and be vulnerable when we sleep.
Sleep is a time when we can keep away from sins, and we can be thankful to Allah to have that time. It is also a reminder of death and the resurrection, for those who pay attention to it and ponder it.
Sleep has been praised by Imam Rida (A): "Sleep is the sultan of the brain, the foundation of the body, and its strength."
Of course this praise is not for excessive sleep. It is not good to sleep excessively (beyond what one needs) or to live in such a way that all one cares about is eating and sleeping or to sleep just out of laziness. Still, a normal amount of sleep can be considered a part of worship (especially in the month of Ramadan), and what is normal or required varies from person to person and at different ages of our lives.
Sleep is part of the natural cycle, and virtually all animals sleep. They sleep at the correct time for their species and are awake at the correct time for their species.
Sometimes it is valuable to reduce sleep for the sake of worship, and of course there is nothing wrong with being awake because one needs to be awake, one wants to be awake, or one simply can't sleep. And of course it is good to be awake on laylat al qadr, etc. But in general in order to be a healthy functioning person, it is good to get the amount of sleep that one needs. I think in general, in industrialized/urban areas, there is much more of a tendency to get not enough sleep (especially in the age of electronics and television) rather than to oversleep.