The character Q is a mischievous, seemingly omnipotent being who has taken an interest in humans. Q's power is limited only in that he cannot overcome others in the Q Continuum, the peer group to which he belongs, and he is never seen being able to actually change a person's mind or make them take any specific action. Otherwise, he can do more or less whatever he wants, which most commonly leads to him annoying others (with or without intent).
Q also has a flair for drama, with a mercurial personality that switches between a joking, camp style and a more ominous and even dangerous manner. While he is boastful, condescending, and threatening, he arguably has humans' best interests at heart, as seen in the series finale, "All Good Things...", in which he causes Jean-Luc Picard to shift through chronological periods, giving him a chance to save humanity. In his portrayal of Q, John de Lancie used Lady Caroline Lamb's famous description of Lord Byron as "mad, bad and dangerous to know" as his inspiration. Q first appears as an antagonist in the series premiere, "Encounter at Farpoint", putting Picard and the Enterprise crew on trial for venturing beyond human ability and threatening humans with annihilation. His next appearance was later in the first season in the episode "Hide and Q", where he desired to have a human enter the Continuum, settling on Picard's first officer, Commander Riker. In later episodes, he becomes more of a trickster. Q evolved into a sympathetic and at times even pitiful character. In "Déjà Q", Q is punished by the Q Continuum by being made mortal; his committing of an uncharacteristically selfless act garners the return of his powers. In the same episode, Q says that Picard is "the closest thing in this universe that I have to a friend." Toward the end of The Next Generation, Q is less antagonistic toward Picard, even, in "Tapestry", apparently saving Picard and helping the captain better understand himself. In the series finale, "All Good Things...", Q gives Picard a "helping hand" in saving humanity.
Picard often thinks of Q as an annoyance, and Q often is surprised by Picard and the other humans he encounters. In "Q Who?", when Picard argues that humans are capable of dealing with anything, Q whisks the U.S.S. Enterprise to the system J-25 for what is presumably the first human encounter with the Borg. Picard resorts to asking for Q to save the ship. Surprised, Q brings the Enterprise home and tells Picard that most men would rather have died than ask for help. It is debated whether Q's interference brought the Federation to the Borg's attention, or whether Q provided assistance by exposing Picard to the Borg, which gave the Federation some early warning; however Guinan (whose people, the El-Aurians, were attacked by the Borg) stated that he did not warn the Federation about the Borg, because without Q's interference the Borg would not have encountered the Federation until they had become peaceful (Q also seems very much an enemy of Guinan, for reasons unexplained). Events later shown in the prequel Star Trek: Enterprise suggest the Borg were already on the way when Q introduced them and Picard to each other. Borg brought back through time in "Star Trek: First Contact" and stranded at Earth's North Pole assimilated a vessel and were able to transmit a message to Borg in the Delta Quadrant at the time, though it would take several hundred years for this message to reach its destination. However, it could also be argued that had Q not introduced the Borg to the Federation, the Borg would not have launched the attack on Earth that ended in the past from whence they sent the signal.
In Q's later appearances on Star Trek: Voyager and Star Trek: Deep Space Nine, he is less concerned with humans and becomes more of a comic relief character. In the DS9 episode "Q-Less", Q at one point goads Commander Benjamin Sisko into a bare-knuckle boxing match, all the while belittling and insulting him. When Sisko loses his temper and knocks Q down, an astonished Q says, "You hit me! Picard never hit me!" Sisko counters frankly that "I'm not Picard." Q responds with a smile, saying "No...you're much easier to provoke."
All seems to be just a game for Q, however, and when characters show genuine compassion or restraint, he will usually admit to being impressed that their "tiny human minds" were capable of such action.