In the Star Trekfictional universe, the Q are a race of near-omnipotent, near-omniscientgod-like beings from a parallel existence called the Q Continuum. They are largely indifferent to the affairs of the non-Q beings living in normal space, with a few exceptions. The most notable of these is Q as played by John de Lancie, a mischievous Q who periodically harasses the crews of starships and space stations.
Other members of the Continuum featured on the series are Q's wife Q, their son q (called Junior by his father, and signified by a lower-case q in writing), Q2 who is a friend of Q, Quinn - a rogue Q who demands to be allowed to commit suicide, and Amanda Rogers who was raised like a human but eventually discovered her true identity. Fans have speculated that Trelane from the original series episode "The Squire of Gothos" was also a Q (see below).
Some episodes have suggested that the Q had evolved to their current state over time, that possibly they were much like humans. Q once suggested that eventually the humans might even advance beyond the Q.
† Note: Many fans have speculated that Squire Trelane was a Q; this formed the basis for Peter David's book Q-Squared. However, this link is only speculation, not canon.
External links
Q (http://www.memory-alpha.org/en/index.php/Q) article at Memory Alpha, a Star Trek wiki
Q Continuum (http://www.memory-alpha.org/en/index.php/Q_Continuum) article at Memory Alpha, a Star Trek wiki
Q Rules! (http://www.worc.u-net.com/alt.fan.q/qrules.txt) - An Unauthorized History by Atara Stein
Q shows Picard his history, and eventual meeting with another omnipotent being called 0 ("Zero"), who Q eventually helps escape from his frozen prison planet in another plane of the multiverse.
Q's attempt to help arrest the four is recognized, and his punishment is relatively light, with Q's rehabilition to include repairing a small planet, the third in distance from a Class G star that had been thriving with dinosaurs.
Q makes several appearances in the novels, as well as, of course, being present on the Enterprise E while Picard and her husband are in the past.
This Q was apparently something of a rebel within the Q race, and his antics occasionally got him into trouble with his fellow Q and served as an inspiration for the Q that the Voyager crew would know as Quinn, who admired his restlessness and inquisitiveness.
Q is one of the most beloved recurring characters on Star Trek: The Next Generation, in large part because of the comedic and dramatic chemistry between actors de Lancie and Patrick Stewart (who plays Picard, captain of the Enterprise).