Q

Q is for... Q!

The Q are often known as an "omnipotent" and immortal species with a great deal of control over space, matter, and time. The Q have been known to travel through time, create alternate timelines, move asteroid belts and stars, change universal states of nature, and teleport with great ease. They have also been able to transfer their powers to other life forms, and have their powers removed by a higher authority in the Q Continuum.

There are, however, concerns about the Q's omnipotence. In the Voyager episode "Death Wish", Q (who later named himself Quinn) informs the crew that the Q are not, in fact, omnipotent:

"You mustn't think of us as omnipotent, no matter what The Continuum would like you to believe. You and your ship seem incredibly powerful to lifeforms without your technological expertise! It's no different with us; we may appear omnipotent to you, but believe me, we're not!"

The Q later known as Quinn - Deathwish

It is in this episode that we are also made aware that the Q had been influencing human history since (at least) the time of Isaac Newton, and that the Q can be made mortal and die/be executed (backing up Quinn's claim that the Q are not entirely omnipotent).

There are also concerns about the initial state of the Q - is has been suggested (both by Q) that they had evolved over countless centuries into the "ultimate form of evolution", and that they had always been as they were, without a beginning.

Q judges - Q2

Being immortal and seemingly omnipotent, the Q soon fell into a sort of stagnation. Having seen, done, and said all that there was, they found no reason to speak to one another or to venture outside of the Continuum. To correct this stagnant state, the Q known as Quinn committed suicide in an attempt to create unpredictable social consequences that would force the Q to interact. Unfortunately, his suicide brought on a civil war within the continuum between the traditional Q and the "Freedom Faction", political idealists led by Q (John De Lancie). These two factions created weapons that could affect even the immortal Q, which resulted in serious damage being done to subspace to such a degree that the Q outside of the Continuum lost their immortality and powers, and many stars were going supernova.

Mating Q - Q and the Grey

The civil war is ended when Q (John De Lancie) mates with a female Q (by touching fingers) and produces a child, something that has not been done in the continuum for over ten millennia. Of course, we know that this child grows to be quite the troublemaker.

Quite accidentally, I have only included pictures from Voyager (the Q appeared in three VOY episodes), and  most of the information gathered for this post is from Voyager as well - this is merely because the Q race was explored more deeply in this series. Q first appeared in the TNG pilot, "Encounter at Farpoint", and the Q appeared many times later - in 8 TNG episodes, and one DS9 episode.

Fun fact: I had always thought that Trelane (TOS The Squire of Gothos) might be a Q - a fact backed up by a book I recently read - Q-squared by Peter David.