This article discusses research showing that some learning can occur during sleep. In this study, researchers exposed subjects to a sound paired with a certain smell that affects breathing during sleep. They did this enough times so that the subjects had the breathing reaction just to the sound alone, even when the smell did not accompany it (think Pavlovian response).
The researchers then tested the subjects when awake and found that they reacted to the sound alone, even when there was no smell along with it. This means that the learning occurred while asleep, as the subjects had no memory of either the sound or smell. Pretty cool, huh?