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.
Fan Nickname: Picard's habit of straightening his uniform is called "the Picard Maneuver" by fans (not to be confused with "the Picard Maneuver" from the episode "The Battle").
Germans Love Counselor Troi: Marina Sirtis has a sizable fanbase in Germany (She gloats in one interview that it's the only place where Brent Spiner doesn't have top billing).
Bob Gunton, aka Samuel Norton, played Chief O'Brien's previous captain in "The Wounded".
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.
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.
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 working 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. According to Stewart, TNG taught him to do good work and have fun doing it. This is mirrored by Picard's final line of the show, in which he joins his crew for a game of poker.
Throw It In: Skin of Evil was Denise Crosby's last aired episode, 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.
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.
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 develop a romance with Worf, but this was scuttled when K'Ehleyr was introduced later the same season. Incidentally, both characters were played by 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".
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.
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.