I've read anecdotes about people who solve technical problems in their dreams and the concept of getting a few more mental hours out of the day is very appealing.
This is one that every russian kid knows from school days:
"I saw in a dream a table where all elements fell into place as required. Awakening, I immediately wrote it down on a piece of paper, only in one place did a correction later seem necessary."
I would consider your Mendeleev quotation as an example of a different, though also quite fascinating phenomenon. What is being discussed in the above article relates to processing sensory input during sleep. The Mendeleeev anecdote is related to memory consolidation/restructuring that occurs during sleep and can cause insight (ie "a mental restructuring that leads to a sudden gain of explicit knowledge allowing qualitatively changed behaviour"[0]), independent of sensory input during sleep. Your Mendeleev reference reminds of a fascinating study[0] that examines the capability of sleep to yield insight because they also reference the Mendeleev anecdote in their introduction. I highly recommend reading the article. It's short, easy to understand, and demonstrates the importance of sleep for problem solving.
This is one that every russian kid knows from school days:
"I saw in a dream a table where all elements fell into place as required. Awakening, I immediately wrote it down on a piece of paper, only in one place did a correction later seem necessary."
—Mendeleev, as quoted by Inostrantzev
http://en.wikipedia.org/wiki/Dmitri_Mendeleev#Periodic_table