Lucid Dream

"''"Often when one is asleep, there is something in consciousness which declares that what then presents itself is but a dream.""

- Attributed to Aristotle, in Hypnogogia: The Unique State of Consciousness Between Wakefullness and Sleep by Andreas Mavromatis

A lucid dream is, simply put, a dream where the sleeping person is aware that he/she is dreaming. By consequence, he/she can exert this awareness over the dream and manipulate it at will.

Anime and Manga

 * In the ending of Kirby Right Back At Ya had Kirby falling asleep and Unlike before when he was awake.

Fan Works

 * In the incomplete Harry Potter and the Wand of Uru by JoeHundredaire/alienyouthct, Harry was plagued by a series of dreams which he thinks may be showing him various alternate futures, and explicitly wishes that they were lucid so that he could ask questions and discover more details.
 * In Astral Journey: It's Complicated, narrator (Emma) learns about this during her coma and partial return to her body.