Okay... let's start with TNG.
Yes, you won't find arcs, per se. In those days, shows were all about syndication, where one can throw any random episode up at any time. So the common method was to have completely self-contained episodes, for the sake of said syndication.
Star Trek, especially in its later years, strained against that. DS9 had to sneak their main series protagonists' introduction into a filler episode to keep it under the radar. Voyager intended the "Year of Hell" story arc to be a season long... but it got cut to a two-parter due to that same difficulty. People wanted to push the boundaries, but in many cases the higher-ups just wouldn't let them,
because television was different in the early nineties.
You can't fault them for their historical placement, anymore than you can't fault silent films for their lack of impressive CGI... since again, they weren't at a point in history where computers even existed yet.
But I digress. For TNG, there are some truly excellent episodes. Here's the short list of the best of the best, the stuff you ABSOLUTELY want to see:
Episode 125: Conspiracy - The goriest episode of Star Trek, and one of the creepiest. See for yourself!
Episode 203: Elementary, My Dear Data - this is a fun holodeck episode. Yes, that's usually a contradiction in terms, but bear with me. It's amusing and enjoyable to see Data get Sherlock Holmes wrong, and the friendship between Data and Geordie is great. Fun and silly.
Episode 208: A Matter of Honor - A Klingon ship and the Enterprise begin a crew exchange program, and Riker is assigned to the Klingon ship. Hilarity ensues. In a good way. It's an action-packed, exciting episode. Top 20.
Episode 209: The Measure of a Man - this episode is excellent and well written, perhaps one of the very first well-written TNG episodes. It's about Data and whether he has rights, or is just a machine. Excellent as actual science fiction. Top eleven.
Episode 215: Pen Pals - An ethical dilemma based on the high-falutin so-called morals of the Prime Directive gets a healthy dose of personification in the form of a little girl Data talks to. It's alright, if you can stand the Prime Directive crap.
Episode 216: Q Who - This is it, the very first Borg story. It's well written, well acted, and all around excellent, introducing a truly frightening opponent. Top 20.
Episode 305: The Bonding - Ronald D. Moore's first script on the show. It's about a boy who's mother was a redshirt and, well, did what all redshirts do in Star Trek. Only this redshirt had a family. And now the crew must deal with the emotional trauma. Plus a hackneyed alien messing with them, as usual. It's very good, even in its diluted state.
Episode 313: Deja Q - So, Q loses his powers, and is exiled aboard the Enterprise. Excellently acted, and well-written. John de Lancie steals the show. Top 20.
Episode 314: A Matter of Perspective - Riker is charged with murder. The holodeck is used for forensic recreations of crime scenes. It's actually good.
Episode 315: Yesterday's Enterprise - When the Enterprise encounters a temporal rift, all of reality is changed... and the Federation is now at war with the Klingons. Retroactively makes Tasha Yar's stupidly done death, and Denise Crosby's departure from the show, worth it. Contender for best episode in the series, or at least in the top five.
Episode 316: The Offspring - Data creates himself a daughter. Becomes a tear jerker, somehow, and convinces me that Data DOES have emotions... even if he doesn't express them or experience them the same way humans do.
Episode 317: Sins of the Father - An episode focusing on Worf and Klingon politics! It eventually gets old, but not in this episode. The beginning of one of the only story arcs in TNG.
Episode 321: Hollow Pursuits - Introduces Reginald Barclay, one of the best characters of the show. A rare comedy episode that works, and focuses, basically, on video game addiction, albeit through holodecks. Great stuff.
Episode 326: The Best of Both Worlds, Part 1 - Contender for best episode in the series, or at least in the top five. The Borg have finally come. End of line.
Episode 401: The Best of Both Worlds, Part 2 - If you don't want to watch this after seeing part one, then there's no hope for you. Top eleven.
Episode 402: Family - Not a regular episode, it deals with the aftermath of the two-parter, and gives Picard some greatly needed extra characterization.
Episode 405: Remember Me - A "puzzle" episode. Something strange is going on, as Doctor Crusher is the only one to remember various people... who soon disappear, never to have existed. Including main cast members. I won't be recommending a lot of these puzzle episodes... but this is a good one.
Episode 412: The Wounded - Introduces the Cardassians, their previous war with the Federation, and a big retcon. Regardless, it gives O'Brien a lot of screentime, and deals with a rogue admiral with PTSD from that war threatening to break a treaty the Federation REALLY doesn't want to have broken... Top 20.
Episode 413: Devil's Due - This isn't so much a great episode as a good piece of actual science fiction. The Enterprise comes to a planet whose god has returned to them... but is all as it seems?
Episode 414: Clues - Another "puzzle" episode, but a good one. The Enterprise crew soon realizes that they've lost an entire day... except for Data. Who refuses to admit it happened. This one's pretty fun, too.
Episode 415: First Contact - Not the eighth film in the franchise. Riker is on a planet observing the populace, who are just about to invent warp drive. He gets caught. A great examination of the human condition, by way of aliens, and the ways humans would react to encountering aliens the same way. This one, again, is actual science fiction worthy of the name. Top eleven, easily.
Episode 421: The Drumhead - Suspicions of terrorism leads to a show trial, and Picard must make the best speech of his career. Very relevant social commentary, scarily accurate in regards to post 9/11 fears. Top eleven.
Episode 425: In Theory - Data gets a girlfriend. Another comedic episode that works, and has (ironically) a very human feel to it. Top 20.
Episodes 426 and 501: Redemption 1 & 2 - Worf's story arc continues, as he gets embroiled in the Klingon Civil War! Top 20.
Episode 502: Darmok - Excellent piece of science fiction, about the difficulties of communicating with a truly alien being, and the joy that comes from learning to understand one another. A contender for best episode of the series, or at least one of the top five.
Episode 503: Ensign Ro - Continues the Cardassian metaplot, introducing the Bajorans and an interesting new minor character. (Hint: she's in the title.)
Episodes 507-8: Unification I and II - Leonard Nimoy and Denise Crosby guest star. Spock, Romulans and the Yesterday's Enterprise/Klingon Civil War metaplot collide!
Episode 509: A Matter of Time - A time traveler from the 26th century comes to observe the crew of the Enterprise as they try to stop a calamity from happening. He won't tell them whether they succeed or not... this is one of the only good time travel episodes in Star Trek history, and decent science fiction as well, dealing with actual themes and such.
Episode 516: Ethics - After a terrible accident, Worf becomes paralyzed from the waist down. He decides he wants to commit suicide... while an unscrupulous doctor wants to perform untested experimental surgery on him. Like the Drumhead, this is an excellent social issues episode, arguing well for all sides.
Episode 517: The Outcast - By modern standards incredibly problematic, not to mention cowardly as heck, but the episode tries to deal with another serious ethical topic: The treatment of homosexuals. Without ever referring to homosexuality once. I actually find the episode reprehensible in its cowardice, but darn it, it was 1992...
Episode 518: Cause and Effect - The third of four "puzzle" episodes I'm going to recommend. This time, the crew of the Enterprise is caught in a time loop, that inevitable ends in the Enterprise's destruction. Can they ever escape? Or will this retroactively be Endless Eight all over again?
Episode 519: The First Duty - Wesley Crusher gets what's coming to him. A court marshal. Finally! Enough said. (Also, the character of Tom Paris, important to Star Trek: Voyager, is introd- wait, what? That's just a character with the exact same backstory, played by the same actor, and NOT Tom Paris? Oh, because it would have meant paying the writer of this episode royalties for every episode of Voyager? Huh. Well, anyway, it's the same person, whatever.)
Episode 523: I, Borg - The Enterprise discovers a single Borg drone, stranded. They begin, uh, talking to him. Very good episode, really.
Episode 525: The Inner Light - Picard is struck by a mind-affecting probe, and wakes up in a world where he's known as someone else. I don't want to spoil it for you, but this, too, is excellent science fiction. It even won an Emmy. A contender for best episode in the series, or at least one of the top five.
Episodes 526 & 601: Time's Arrow 1 & 2 - 19th century period piece, as Data tries to get back to the 24th century. Kinda silly though, I mean, he is an android. Maybe he could go back the long way...
Episode 602: Realm of Fear - Barclay returns in his third, and second best, episode. This time, Starfleet's Most Neurotic Officer must come to terms with his transporter phobia... the hard way.
Episodes 610 & 611: Chain of Command 1 & 2 - Are you noticing a trend here? The two-parters are actually pretty good, up until now, and we're getting them even outside of season finales. This one is excellent, as it continues the Cardassian metaplot, and Picard gets captured, and a new, hard-line captain takes the helm of the Enterprise. Chain of Command 2 is a top eleven episode.
Episode 615: Tapestry - Captain Picard dies on the operating table. Q sends him back to relive his Academy days. Q stops being a trickster, and finally lives up to his promise to be something... profound. Top eleven episode.
Episode 624: Second Chances - Re-examining a site where Riker almost got trapped eight years before, the Enterprise discovers... another Riker, stranded all this time? An excellent character piece on how differing circumstances changes a man. I'm tempted to put this in the top eleven, but... well, definitely top 20.
Episode 625: Timescape - The fourth and final "mystery" episode that I'll recommend. After going to a conference on planet Whatever, Picard, Geordie, and Troy discover the Enterprise frozen in time... and apparently being attacked by a Romulan War-Bird!
Episode 711: Parallels - Worf returns to the Enterprise after winning a tournament, only to find that reality keeps shifting, in small but slowly growing ways... great character piece for Worf, and has one of the most chilling moments in all of Star Trek, when you see what would have happened had the Borg won. It's in the top 20.
Episode 712: Pegasus - Riker is faced with his past when his first captain -now an admiral- comes on board the Enterprise on a secret mission... one that may fray the relationship between Picard and Riker.
Episode 715: Lower Decks - This episode focuses on a group of lower-rank officers. For once, we get to see how the stars of the show are seen by the people under their command. Stars a character from The First Duty, and continues the Cardassian metaplot. Top 20.
Episode 716: Thine Own Self - While venturing amongst a primitive race, Data is damaged, losing his memory. And the understanding that the metal material he's carrying with him is radioactive.
Episode 724: Preemptive Strike - Ensign Ro finds herself conflicted between Starfleet and the Maquis, in this continuation of the Cardassian metaplot.
Episode 725-726: All Good Things... - The finale of Star Trek: The Next Generation spans from the beginning of time to Picard's own future, as we discover that the Trial Q started in the series premiere continues to this day, and Picard must save all of time and space. A contender for best episode of the series, or at least in the top five.
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Now I know what you're asking yourself: "Why top 11?" Because, like the Nostalgia Critic was wont to say, I go one step beyond.
To finish up, I'll also list my absolute favorite episodes, in order:
The Top Five: Any of these could be the best episode, and all far exceed expectations. They are the heights that this franchise can accomplish. They are Star Trek at its absolute best.
1.) The Best of Both Worlds part 1
2.) Yesterday's Enterprise
3.) The Inner Light
4.) Darmok
5.) All Good Things...
The Top Eleven: To round up the rest of these, you've got some excellent character pieces and works of science fiction in general. Any show would be lucky to have them.
6.) Tapesty (Was only edged out by All Good Things... because it's the series finale. Otherwise this episode is easily it's equal)
7.) The Measure of a Man
8.) Chain of Command 1 & 2
9.) The Best of Both Worlds part 2 (Unlike other two-parters, I count this one separately. Still excellent, but it has to compare to the first half...)
10.) First Contact
11.) The Drumhead
The Top Twenty: Not quite as excellent as the very best... but some of them are contenders. I can see other people placing many of them in their own personal top ten lists. Don't put their number to heart, they're all about equal to me.
12.) In Theory (I love this episode, personally. It was a contender for 11.)
13.) The Lower Decks
14.) Parallels
15.) Redemption
16.) Q Who
17.) Deja Q
18.) Second Chances
19.) A Matter of Honor
20.) The Wounded.
Edit: Notice that only one of the episodes I consider even above average are from the first season. There's a very good reason for this.
Edit 2:
Bonus Round! 0Megabyte's Top Five Most Hated TNG Episodes!
In descending order of badness:
Episode 102: The Naked Now - The crew of the Enterprise is infected with a virus that makes them act out of character in "silly" ways. This is the second episode of the series, before we've really had time to establish said characters. It's also a total retread of an Original Series script. Pain. Just pain.
Episode 201: The Child - Pretty horrid, when you think about it. Troy is impregnated against her will, and it's treated with all the sensitivity of a pie in the face.
Episode 714: Sub Rosa - Sorry, Jonathan Frakes. I like you well enough as a director, but this was probably the third most boring hour of television I've ever encountered. Dr. Crusher hangs out on a planet modeled on Scotland. And gets seduced by a ghost who's haunted her family for genera- zzz...
-Oh! Sorry, I fell asleep there.
Episode 122: Skin of Evil - Killed off Tasha Yar, because Denise Crosby didn't believe in the series. Considering how terrible the first season was, who can blame her.
Yes, Yesterday's Enterprise and the future episodes following the metaplot DO redeem the fact that Tasha Yar died... and if Denise Crosby had stayed on, one of the very best episodes of TNG could not have existed. And at the same time, had she stayed on, Michael Dorn as Worf may not have been able to develop the way he did.
And yet... Crosby showed later that she could be a very good actress, and having her around when the show was good, when great stories could be made about her... it's sad to think about what might have been.
Episode 104: Code of Honor - This episode is part of the reason Denise Crosby could think of leaving this series. It's incredibly offensive, for reasons that enter real-world territory.
Edit 3:
C-c-c-combo Breaker! 0Megabyte's Top Five Most Hated TNG Episodes 2: Dishonorable Mentions!
In no particular order:
Episode 222: Shades of Gray - This isn't actually an episode of TNG. This is a clip show made up of other episodes of TNG. Even the bad ones are better than this. It would be in the top five... but alas, it doesn't count as an episode. Heck of a season finale, I'll say...
Episode 719: Genesis - All I have to say is this:
Good night!
Episode 217: Samaritan Snare - Possibly the most annoying race in Star Trek history is introduced here. Later on, Lore, Data's brother, is found by this race, and reappears years later wearing their clothes.
For the record, Lore is a mass-murdering creep with daddy issues.
And yet I can't help but feel a little sorry for him... he did have to spend years with the Pakleds. Isn't that punishment enough for any crime?
Episode 212: The Royale - Incredibly boring. the crew finds a thingie in space that does a thingie and some of them get trapped in the thingie and I dunno, stuff happens I guess? I can't seem to pay any attention to it. It's like a run-of-the-mill Voyager episode, but sillier, somehow.
Episode 218: Up the Long Ladder - Wow, incredibly annoying and offensive Irish stereotypes, and blatantly cruel actions by Captain Picard, that go against the spirit of the only good parts of the Prime Directive. (You know, the part about not using your greater power to take advantage of less powerful cultures, or interfere with them for your own gain... yeah, that part can be trod all over. But in other episodes, heaven forbid you try to give a vaccine to a civilization facing extinction if you don't. That would be wrong. *snerk* )
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Sir Patrick Stewart does not have any additional authority, he's just cooler, and by extension that makes his character cooler.
