Encounter at Farpoint
Hide and Q
All Good Things
This troublesome pest has made the most appearances of any other adversary and is a mixture of malevolence, indifference, genius, humor, and inconsideration, the latter he brings in abundance being he always shows up uninvited and outstays his welcome.
The Enterprise encounters him first on their first mission to Farpoint. He inconveniences the crew by disrupting their mission and putting members of the crew on trial for the crimes of humanity in a showy staged courtroom play containing cheering rabel.
The Q, AKA The Q Continuum, is a collection of highly advanced beings that appear to be omnipotent and possess the power to manipulate space, time, and matter. This member is rogue and enjoys tormenting creatures of less strength and power. This gets him in trouble with the Q council and he gets banished from the continuum. He seeks refuge on The Enterprise as a full humanoid with no special powers except his intelligence and ability to annoy the hell out of people.
He has both caused the Enterprise grief and saved them from destruction. In "Q-Who," he shows them what lies ahead, a race of beings whose only goal is to consume and destroy. Angered that the captain refuses his offer to become a member of the crew as a guide to the universe, he sends the ship hurling into the Delta quadrant. Here, we are introduced to the Borg, who become the most dangerous threat the Federation has ever seen. After undergoing excessive damage to their ship and the loss of over a dozen crew members, Q brings the ship back to their own space out of harms way. Q tells Picard that what's out in space is wondrous, but not for the timid. Picard realizes what Q actually did was "give us a kick in our complacency."
Q's most important encounter with the crew is in the series finale where he helps Picard save humanity by undoing research Picard does in the future on an anomaly in space that creates a time distortion that reverses linear time.
He has fun for his own pleasure as well, sending the senior staff into Sherwood Forest to rescue a love interest of Picard's. Each crew member plays a role in the famous story about Robin Hood, with Picard playing the lead role. In "Hide & Q," he plays a game of cat and mouse with the crew using "vicious animal things" and reenacting a civil war with Q as a Napoleon type figure.
This warrior race was first introduced in the original series. Mark Lenard, noted for playing Spock's dad, appeared first as a Romulan warrior in "Balance of Terror." Since then, the Romulans have been a staple to the Star Trek franchise.
Not all Romulans are conquerors, some in fact preferring to avoid war, especially unnecessary and costly ones. In "The Defector," a Romulan ambassador tires to stop a plan of conquest and is betrayed by Commander Tomalak. In "Face of the Enemy," a Romulan soldiers is helping transport resistance fighters to Federation space. And Spock makes an appearance in "Unification," as a goodwill ambassador working with an underground movement on Romulus.
Another war like race, the Cardassians major nemesis are the Bajorans. Each side is secretly building up an arsenal. The Federation is trying to maintain peaceful relations with them while keeping a close eye out for their transport ships and colonizations. In "Chain of Command," Captain Picard gets kidnapped and tortured by a Cardassian guard. Picard is used as a bargaining chip to stop the Federation from investigating new biological weapons. The Cardassians are forced to back down when Captain Jellico sets up explosive beacons across their path to stop them from attacking a colony.
Not the brightest bunch, the Ferengi's main philosophy is profit. They are the prime example of vulture capitalists. They are a mixture of stunted intellectualism, greed, misogyny, and general annoyance. In "The Perfect Mate," a few renegade Ferengi's try to steal the bride to be of an ambassador after their offer to buy her from her guardian for a bag of precious metals fails. In "Rascals," another rogue band tries and fails to take over the Enterprise and use it's crew and family members as slave labor to mine for gems.
Introduced to the Federation by Q, this race are a mixture
of biological and artificial mechanical parts. Q called them the
ultimate consumers. They aren't interested in forming
relationships or exchanging ideas. They are only interested in the collection of other species technology
and their bodies for assimilation into their collective. They are the biggest threat the Federation has faced. In "Descent," we see what can happen to them when one Borg becomes individualized and reintroduced into the collective. That is their weakness. They are one collective mind. Conjoined minds thinking individually causes them confusion and chaos. When Lore took lost Borg under his leadership, his main objective was to rid the universe of biological humanoids and experimented on Borg to find ways to turn them into entire mechanical beings like him. Lore was defeated and the colony got a new leader---Hugh.
The remaining Borg collective who weren't affected by the virus of individualization were ultimately defeated in "Star Trek: First Contact" when their queen was destroyed.