"All I have to do is dream ... " and other breakthroughs

There have been a number of reported cases of creative inspiration and even scientific problem-solving while people were asleep. These examples range from Kekulé to Paul McCartney and various webpages have been devoted to the topic (some of them selling dream-related products) http://www.brilliantdreams.com/product/famous-dreams.htm
http://www.dreamtree.com/Culture/Famous.htm

Meanwhile a fairly recent paper from a researcher at Harvard Medical School aims to approach the topic in a more rigorous fashion:

http://www.asdreams.org/journal/articles/barrett3-2.htm