Acting for Two: Time Squared (Patrick Stewart plays two Picards). Second Chances (Jonathan Frakes plays two Rikers). Any episode with Data & Lore or their "father" Dr. Noonien Soong. (Also see the episode Brothers which was Acting For Three (including one stint in enough make up to make a Klingon's actor cry.) And let's not forget A Fistful of Datas, where Data plays...a fistful of Ancient-Western stock-characters.
Similar to how Sisko does with baseball, Picard enjoys using Shakespeare as a metaphor for the human condition. Of course, everyone knows about Stewart's background in Shakespearean theater; he quotes Hamlet in "Hide And Q," and he even plays a dual role as Michael Williams in Data's holodeck play ("The Defector").
Brent Spiner was primarily a comedic actor before being cast as Data. Of all the TNG regulars, Spiner probably goofed off the most between takes, which is why Data is always wearing a semi-menacing grin in behind-the-scenes footage. However, he got to cut loose in "The Outrageous Okona", which had Data practicing his Henny Youngman routine in a comedy club.
TNG had a minor in-show example: In "Descent, Part II" the Enterprise is forced to hide within a star's corona by using an experimental shield. The lieutenant at Tactical doesn't think that the shield will work, but is proven wrong. The actor played a different character in a previous episode who tried to make it appear that the shield didn't work.
In "Sarek," Wesley gets ticked at Geordi and taunts him by saying, "At least I'm not spending the night with a good book, like some people!" Geordi seems to take this remark rather personally.
In "Half A Life," David Ogden Stiers guest-stars as an alien scientist doing research work on the Enterprise. One of his report readouts is attempt number 4077.
Banned in China: "The High Ground" got banned from broadcast in both the UK and the Republic of Ireland due to a line about Ireland being reunited in 2024 following a successful "terrorist" campaign.
"Conspiracy" was banned for a time in the U.K. because of the infamous "exploding Remmick" scene.
Descended Creator: Roddenberry's wife Majel Barrett, who also played Lwaxana Troi, owned a great deal of the rights and was one of the chief executives owning Star Trek after her husband's death.
Directed by Cast Member: Stewart, Frakes, Burton and McFadden all directed episodes. McFadden also choreographed the dance sequences in "Data's Day", Frakes directed two of the movies, and Dorn directed several episodes of DS9.
Executive Meddling: Is what got Patrick Stewart an audition in the first place. The casting director saw him in a play and wanted him to try out, but Roddenberry was against it - feeling Stewart was too old and too bald to play Picard. Rick Berman admitted to also having doubts, but he was at least willing to give Stewart a shot. Berman, the casting director and production manager Robert H. Justman kept pressuring Roddenberry until he finally relented to seeing Stewart audition.
Mark Alaimo appeared as a minor Rubber Forehead Alien in Season 1's "Lonely Among Us," Romulan Commander Tebok later that season in "The Neutral Zone," Cardassian Gul Macet in Season 4's "The Wounded", and a 19th century gambler in Season 5's "Time's Arrow" before taking on the role of Deep Space Nine's Gul Dukat.
The late Andreas Katsulas, who played Romulan Commander Tomalak, was Ambassador G'Kar on Babylon 5, and Fred Sykes, the one-armed man in The Fugitive.
This show and Batman: The Animated Series share cast members, two of whom are Diana Muldaur (Dr. Pulaski) as Dr. Leslie Thompkins and John de Lancie (Q) as one of the Penguin's henchmen in "Blind as a Bat." Another would be David Warner, who played Ra's al-Ghul in Batman and Gul Madred, Picard's interrogator, in Chain of Command.
Likewise, Gargoyles was comprised mostly of TNG cast members, including Frakes (Xanatos), Spiner (Robin/Puck), Sirtis (Demona), and VOY's Kate Mulgrew (Titania), among others. The full list is on That Other Wiki. The Brazilian Portuguese dub chose to give Picard's voice to Xanatos.
In "Coming of Age", Wesley attends a Starfleet Academy exam with two other hopefuls, including a young Vulcan. This is Tasia Valenza, best-known for voicing Sniper Wolf in the best-selling Metal Gear Solid and Poison Ivy in the Batman: Arkham series.
Michael Dorn often resembles his character during cast reunions. Also, having to modulate his voice for Worf's baritone caused Dorn's real-life (nasally) voice to dip several octaves.
In the William Shatner documentary The Captains, Patrick Stewart's behind-the-scenes experiences at TNG share an odd similarity with his character. Stewart, who was stressed out over succeeding the stars of TOS and his long hours, got the cast together and told them to quit goofing off between takes ("We're not here to HAVE FUN!!"); his castmates never let him live that down. In the long run, TNG taught him to do good work and have fun doing it. This is mirrored by Picard's final line of the show when he joins the Bridge Officers' poker game.
The Tricorders and to a lesser extent the computer PADDs seen in this version of Trek inspired all kinds of similarly-sized, touchscreen-powered devices, such as tablet PCs, Palm Pilots and the iPhone. THE IPAD IS FROM THE FUTURE!
The Merch: Next Gen had two distinct toylines. The first, by Lewis Galoob, came out during the first few seasons. It featured 3.75" figures (in scale with Star Wars and smallish, die-cast vehicles including an Enterprise whose saucer detached. A few years later, Playmates Toys came out with its own line, which...Let's just say that Next Gen was a landmark moment in toys, even more so than Star Wars. The figures boasted superior sculpting and articulation (though sitting down looked slightly unnatural), there were aliens and villains right in the first run, and the line made incredibly creative use of electronics, with sound effects taken directly from the show! What's more, the show itself provided more than ample inspiration for variants, including the "Holodeck Adventures" line. Playmates held onto the license with its teeth, providing lines for Deep Space Nine, Voyager, the Original Series (which got its own badass boxed-set), the movies, Enterprise, and the first J.J. Abrams movie.
The Other Darrin: Spot. Yep. Data's first feline friend was a long-haired Somali, while later ones are played by a generic short-haired tabby. This has caused some Trek authorities to joke that Spot is a shapeshifter in disguise, or else lost his fur in a transporter accident.
Playing Against Type: TNG had a habit of casting noted TV "bad guys" in benign or heroic roles. Jonathan Frakes is undoubtedly the biggest example, as his career up that point had been almost entirely villain roles. Others include Harry Groener as Tam Elbrun, Ronnie Cox as Captain Jellico, Christopher McDonald as Richard Castillo, Robert Knepper as Wyatt Miller, and Spencer Garrett as Simon Tarses. (No such luck for Marc Alaimo, though; he played four bad guys!)
Promoted Fangirl: Whoopi Goldberg was a huge fan of the original series and has specifically named Nichelle Nichols as her inspiration for acting. Just before the second season entered production, she called Roddenberry, saying "I am a Star Trek fan, I was a Star Trek fan long before I was ever Whoopi Goldberg and I'm wondering if there's some part I can play in your show?" Roddenberry was so impressed that he re-wrote the bartender character he had intended to introduce for Goldberg.
Real Life Writes the Plot: "The Defector" was supposed to open with another Sherlock Holmes pastiche, but legal issues forced the writers to retool it into a holodeck simulation of Henry V. This doubles as foreshadowing: Jarok, like King Henry, is forced to go undercover as a 'commoner' in this episode.
"The Best of Both Worlds" introduces a job opening for Riker on another ship, as well as a new female commander for him to butt heads with. The showrunners were grooming Riker to take over as Captain if Patrick Stewart didn't want to return.
Reality Subtext: LeVar Burton would often get headaches from the devices on his temples that were used to hold the VISOR in place. Likewise, Geordi would ocassionally mention headaches as a side effect of wearing the VISOR.
Probably an aversion with Worf; the DC Star Trek comics had long featured a Klingon in Starfleet named Konom, but his backstory and character are very different from Worf's and Roddenberry probably had a similar idea independently.
Data is derived from the character Xon from the cancelled Star Trek: Phase 2. Xon was a full-blooded Vulcan, the idea being that he would provide a contrast to the vanished Spock—whereas Spock was always denying his human side and embracing his Vulcan, Xon would already be secure in his Vulcan-ness and thus be more intrigued and curious about understanding human emotions. This eventually mutated into the idea of an emotionless android seeking to achieve those human emotions.
Famke Janssen as Kamala, the empathic metamorph who bonds with Picard in "The Perfect Mate." Famke Janssen and Patrick Stewart would later star together in the X-Men film series as Jean Grey and Professor X, respectively.
Hey, it's Zefram Cochran as Prime Minister Nayrok in "The Hunted" (and Zaglom Shrek in "Birthright," Pts. 1 & 2, even though you can't see his face in that one)!
Hey, that Ferengi Dr. Farek in "Menage a Troi" sure sounds a lot like Neelix. (He later played another Ferengi on Enterprise.)
Romance on the Set: Patrick Stewart, on the lookout for the next Ex-Ms. Patrick Stewart, dated Jennifer Hetrick (Vash) during Seasons 3 & 4. They were briefly engaged during "Q-Pid", but nothing came of it.
"Skin of Evil" was Denise Crosby's last aired episodenote other than her coming Back for the Dead in an Alternate Timeline in "Yesterday's Enterprise", with her character being killed off. In the previous episode, "Symbiosis" (which was actually filmed later), she's in the background at the end, as Picard and Crusher enter the turbolift. Just as the doors close she waves goodbye to the camera.
In "QPid", Vash has been transformed into Lady Marian by Q. As they were filming the scene where she paces back and forth in her cell, Jennifer Hetrick tripped over her dress. The director left it in reasoning that a 24th century woman would not be used to walking in 12th-century finery.
Troubled Production: As per usual with Trek, getting the show on the air was extremely taxing. Gene was quarrelsome, in ill health, and fans of The Original Series were more than usually scrutinizing. The prototype uniforms smelled bad (spandex retains bodily oils more than the newer cloth uniforms) and gave the actors back problems. After three seasons, two actors (Crosby and McFadden) had had enough, and Patrick Stewart was in the middle of contract re-negotiations. General consensus has it that the audience response to "Best of Both Worlds" revitalized the program, although the addition of Whoopi Golfberg and return of Gates certainty helped.
Robin Williams was offered the part of the time-traveling "Dr." Berlinghoff Rasmussen in "A Matter of Time", but he was busy working on Hook at the time, so the role was given to Matt Frewer.
Stewart auditioned for TNG three times. Once for Data and twice for Picard. Once bald and once wearing a hairpiece.
Edward James Olmos was offered the part of Jean-Luc Picard, but declined due to being constrained by contractual obligation. Over time this story has morphed into Olmos being considered for the lead in Voyager, and other such rumours.
Marina Sirtis and Denise Crosby were originally going to play Yar and Troi respectively, but switched roles at the last minute.
The Borg were planned to be insectoid aliens but the special effects budget wouldn't cut it. The concept was reused for the Jarada, who we never see on-screen.
The writers considered crashing the ship's saucer section on a planet as the cliffhanger ending of Season 6, but the budget didn't allow for it. This was eventually used in Star Trek: Generations instead. Separating the saucer itself was planned to be a much more common tactic, but again effects expenses meant it was only used four times. In addition, halfway through season one it had become painfully obvious that saucer separation was time-consuming and destroyed the pacing, a major issue when it was supposed to happen halfway through dramatic battle sequences.
Wesley Snipes was considered to star as Geordi LaForge. Tim "Tuvok" Russ also auditioned for the role. He came that close to getting it, too.
Among the actors that auditioned for Riker were Jeffrey Combs and Vaughn Armstrong - both of whom became pretty well-known to viewers regardless.
How much better would "The Outcast" have been if the actors playing the sexless J'naii were male instead of female? Jonathan Frakes criticized the staff for not doing that and making the message of the episode that much stronger.
For "All Good Things...", the writers considered revisiting "The Best of Both Worlds" in addition to the other three time periods.
Dr. Selar (from "The Schzoid Man" and repeatedly referenced) was originally intended to be a recurring character and would develop a romance with Worf, since there was a drought of Vulcans on the show and pairing one up with a Klingon sounded interesting. But this was scuttled when K'Ehleyr was introduced later the same season. Incidentally, both characters has similar names (seriously, try sounding them out) and were played by Statuesque Stunner Suzie Plakson.
The Enterprise was originally going to be the seventh rather than fifth ship to bear the name, and was referred to in the script as the Enterprise Seven rather than the Enterprise-D we know and love.
The writers considered bringing back Denise Crosby as Tasha in one of the alternate universes in "Parallels", but decided against it, feeling it'd be redundant after "Yesterday's Enterprise".
The Q Continuum were originally going to be many people with the same face. This portrayal is rather apparent in "Encounter At Farpoint," with each change of costume Q goes through usually resulting in a change in attitude and demeanor. However, by Q's next appearance, this particular idea seems to have been dropped, with Q acting as a single individual, and later episodes (and Star Trek: Voyager) introduced additional members of the Q Continuum.
The writers didn't know what to do with Troi in Season 1, even omitting her from four episodes just to save themselves the trouble. Marina Sirtis has said she was nearly let go after Season 1 because of this. She was only kept on because Denise Crosby had already left and Gates McFadden would soon decide to leave.
At one point Wesley Crusher was planned as a female character named Leslie Crusher, as the TNG creators thought the teenaged boy genius was too much of a cliché. (They were probably right.) Although considering that a female genius would have been Mary Sue, it was kind of a no-win situation.
Ronald D. Moore considered bringing Captain Jellico back to be the commander of the Enterprise in the Alternate Timeline presented in the episode "Tapestry".
One of the people who was considered a favorite for the role that eventually became Tasha Yar was Rosalind Chao, who later portrayed Keiko O'Brien.
Word of Saint Paul: The Star Trek The Next Generation Technical Manual, in its entry on the Captain's Yacht, includes an out-of-universe sidebar that says "Patrick Stewart informs us the yacht is named Calypso after Jacques Cousteau's vessel", in a way that suggests that, as far as the writers of the Manual are concerned, he should know. This was never confirmed on screen, since the Enterprise-D yacht was never used (or even confirmed to exist), but was nodded to in Star Trek: Insurrection, where the yacht on the Enterprise-E is called the Cousteau.
Also from the technical manual, Rick Sternback had a pet idea for "Cetacean Ops" — literally, navigation research that's being handled by a dozen dolphins being overseen by a couple of whales — in huge underwater tanks throughout the ship. It got a mention in "The Perfect Mate", but goes otherwise unregarded by other writers.
Urban Legend of Zelda: The operator's manual for the Star Trek: The Next Generation pinball mentions a "secret Video Mode" in the gamenote allegedly a version of Breakout, and there are two operator settings to control it. Problem is, no one knows how to activate it, and it's unclear if the mode is actually enabled in the final game or not. It can sometimes be seen on the display in the game's attract mode, however.