Dream
From Memory Alpha, the free Star Trek reference.
A dream was a series of sensory imputs and emotions involuntarily occurring in the mind during REM sleep.
AIs sometimes had the ability to dream added to their programing. Noonien Soong added the ability to dream to Data. (TNG: "Birthright, Part I")
In 2367 the crew of the USS Enterprise-D went slowly insane as they were unable to dream while trapped in a Tyken's Rift. (TNG: "Night Terrors")
Worf once commented that Klingons dream about "things that would send cold chills down your spine and wake you in the middle of the night." (DS9: "Rejoined")
In 2373 Captain Jean-Luc Picard experienced a terrifying dream about his experiences with the Borg. The dream was apparently induced by the Borg's proximity. (Star Trek: First Contact)
In 2374 the USS Voyager encountered the dream species, a species of aliens that lived out their lives in dreams. (VOY: "Waking Moments")
In 2375, Nog asked Vic Fontaine if he dreamed when his program was off. In response, Vic only smiled ambiguously. (DS9: "It's Only a Paper Moon")
In 2376, the Doctor added a daydreaming subroutine to his program. (VOY: "Tinker Tenor Doctor Spy")
[edit] Background
Although stated as such in TNG: "Night Terrors", REM sleep is not the exclusive purview of dreams - it is simply the most common time to dream. 5-10% of people who are woken during non-REM sleep also report dreaming. We can perhaps forgive Crusher being inexact as she was impaired by the effects of the Tyken's Rift.
