Dan: So Star Trek and Next Gen are about a resource rich society that is in such a creative rut they will send the Enterprise, humanity's finest ship out to unexplored corners of space just to find new life and new civilizations. Novelty is the most precious commodity there is! This is a profoundly bored people, so jaded, that they will load up their children and women onto a heavily armed warship and send it just out... just go! Just go somewhere and find me something interesting and tell me about it?!
SF Debris believes that Roddenberry's vision of Trek seems to be that in the future, Earth is a Marxist dystopia ruled by Pod-People. Stardestroyer.net has a similar argument in a bit more depth.
While it is true that the series (focused as they are on Starfleet) do not show much of civilian lifestyles in the Federation, what we do see actually implies a rather high standard of living, and quite a diversity of lifestyles, especially when the colonies are factored in. For example, Beverly Crusher's grandmother lived on a colony where everyone was basically doing LARP of life in the pre-industrial Scottish Highlands (with hidden technology maintaining things like the weather). So there is a definite absence of stereotypical Marxist conformity. If anything, people appear to cluster in "lifestyle communities" that meet their personal preferences.
The theory that The Federation is actually The Empire, simply using the Benevolent Alien Invasion to gain new members and extend it's own power. Some point as evidence to in Insurrection, they are recruiting races who've had warp for only a year simply to serve as Cannon-Fodder for the Dominion.
This may very well be a case of Truth in Television though. A common argument floated by anti-Trek commentators is that this future society is so bored and jaded that they have nothing better to do than live out fantasies in holodecks rather than going out and doing anything interesting themselves. However, in real life, early 21st Century America, many millions of people obsess over television (ahem), movies and the internet. People fixate on watching sports they do not actually play themselves, immerse themselves in fictional media, or (for those seeking a little more verisimilitude), turn to so-called "reality TV" to watch other people who apparently have more interesting lives than the viewer does.
A somewhat less dystopian interpretation of the Planet of Hats present in the show is simply that the nature of the stories being told usually means we're seeing mainly planetary leaders and members of the military, all of whom have been trained to act in a way that the elites of their society consider ideal. Notably the series that suffers the least from this trope is DS9, which takes place in a setting that attracts a fair number of civilian workers and merchants.
While not exactly unpopular, the franchise isn't exactly hot in Latin America, despise thetwo first series are the very well known series of the franchise there, partly because of excellent voice acting of both series. The only exception on this rule is Spock, who is the most popular character of the whole franchise in Latin America, even more than Kirk.
Awesome Music: Various theme songs (plus all the live-action series - with the exception of the original - have either been nominated for or won music Emmys, and there's an entire website and book about the music.
Lots and lots and lots of them—count on this to happen basically every time a new series comes out; but most famously Picard / The Next Generation vs Kirk / the original series, which has entered into Pop-Cultural Osmosis.
The old Trek fandom is absolutely split on the new movies. On one hand, the movies are critical and financial successes, and brought a renewed interest in the franchise from young people, actually making it somewhat cool to be a Trekkie for once. On the other hand, the movies were less science-y and more fantastic, something the older fans claim is "not what a real Star Trek movie should be." Expect a massive flame war if the subject is so much as touched upon on a Trek forum.
Contested Sequel: Star Trek XI (referred to by some fans simply as 'the Abrams film' or similar) has caused a Broken Base within Star Trek fans between people who only like the old Trek, people who only like XI, and people who like both.
Creator Worship: The Great Bird of the Galaxy himself. Rick Berman, Ronald Moore and J. J. Abrams are a bit lower on the hierarchy. Brannon Braga is, unfortunately, often villainized for what happened with Voyager and Enterprise.
Escapist Character: Captain Kirk is a bold space adventurer that leads a life of excitement that involves discovering new worlds, romancing sexy aliens and outwitting all sorts of alien baddies. Further enforced in the movies when his retirement from active captaincy is treated like a mid-life crisis and in his final adventure, he admits to Picard that his life only had meaning when he was captain of the Enterprise, driving home how liberating his life of adventure and excitement is.
Franchise Original Sin: Most of the faults found Voyager and Enterprise were already very present in the much-lauded middle seasons of The Next Generation, and some can even be found in The Original Series; things like the anomaly of the week, the malfunctioning holodeck, the evil versions of regular characters, the shuttle crash plots, and the B-plots that feel like a soap opera. But it wasn't until later in the franchise that they really started to grate on viewers, since it finally started to seem like the same thing over and over again.
Ho Yay: Every series has at least one hugely popular slash pairing, and sometimes more than one. Slash fans will insist these characters want nothing more than to do each other, no matter how heavily contradicted by canon.
Kirk/Spock (or Spirk) is the original Slash pairing.
Archer/Reed, Tucker/Reed and Reed/Hayes from Enterprise.
Hilarious in Hindsight:: In the 30th anniversary special, there is a skit featuring the cast of Frasier serving on the USS Voyager under Janeway. At one point, a Klingon beams aboard with the dog, which had been digging up azalea bushes on the Klingon homeworld. Janeway remarks, "Now you see why we shouldn't have pets on starships".
Newer Than They Think: Casual fans often assume that elements of the setting that were introduced in the movies or later series were present in the Original Series. Usually, it's reasonable to assume that these are changes that happened to Federation society over time, but fans tend to assume they were always present. One of the most notable is the idea that the Federation is a moneyless society. The first mention of this is as a throwaway joke in Star Trek IV. There's no evidence of it in the Original Series, and several episodes (Mudd's Women, The Trouble With Tribbles, The Devil In the Dark) would make no sense or at least have gaping plot holes if this were true.
This also applies to the Roddenberry "No Conflict" rule. All Trek fans know that Roddenberry didn't want his humans fighting with each other (though really it was "petty bickering" he didn't want to see) because he wanted to portray us as an "adult race" rather than the child race we are now. But the application of this rule has fans confused. Most seem to think it applies to Star Trek as a whole, while the fact is that Roddenberry came up with this rule while creating Star Trek: The Next Generation. The rule does not apply to the original series or any series set prior to it, making it much ado about nothing when the rule was tossed out for Star Trek: Discovery.
Older Than They Think: Interstellar transporters were featured as early as the TOS episode "Gamesters of Triskelion"
The Problem with Licensed Games: Star Trek has been notoriously variable with the quality of its forays into interactive entertainment - partially because distilling the essence of the best episodes of the series into a truly interactive format is goddamn hard. The "best" Trek games to date have been somewhat more combat-focused than many of the shows really were. Of course, the fact that the license keeps bouncing between hands and developers (unlike LucasArts, who've been refining their Star Wars offerings for the better part of two decades now) has not helped matters in the slightest.
Sequelitis: it began with the very first episode of Voyager, but by the time Insurrection rolled around, even major critics were noting that the franchise was taking a fairly serious and noticeable dip in quality. Enterprise and Nemesis are "credited" with coming within a whisper of killing the franchise (Nemesis being the only Trek film in history to not turn a profit); the reboot salvaged it and its sequel received very good, but not as great reviews than its predecessor.
The films are famous for going back and forth (see Star Trek Movie Curse.) The series, however, follow a much more consistent path. The Original Series was something of an uneven novelty, thanks to inconsistent writing. Next Generation was considered an Even Better Sequel. Deep Space Nine was "different, but still good."Voyager is where the franchise started to unravel, and Enterprise is where it finally came apart.
Heterosexuality is virtually universal. Exceptions to this are rare and always involve alien species in some way. Even bodiless Energy Beings seem to have gender identities and are depicted as heterosexual. Q jokes about appearing to Picard as a woman, but never does so (although he appears in nonhuman forms several times). He also has a long-term (billion year) Q "girlfriend", with whom he has a son who is a stereotypical heterosexual horny teenager that is obsessed with females even from the "lesser" species. While Interspecies Romance is quite common to the point of being expected, any deviation from heterosexuality is definitively explained by Bizarre Alien Biology. The only episodes which depict ordinary humanoid characters being other than straight in an ordinary way are those set in the Mirror Universe whose whole set-up is "evil is dominant" (and the depictions often tend to shallow Girl-on-Girl Is Hot pseudo-lesbian fluff to titillate fanboys). Arguably, stuff like this were done to get past the censors, where they could get away with showing gay stuff as long as aliens are involved and not humans (Gene Roddenberry always wanted to show gay humans, but was always thwarted for obvious reasons). This topic has been much discussed, including on the Other Wiki, Star Trek's own Memory Alpha, as well as other essaysand articles. This is finally averted in Star Trek Beyond where it's revealed that in this timeline, Sulu is gay and has both a husband and a daughter,note Although that one has its own problems, in that the writers said they did it out of homage to George Takei... who always said he played the character as being straight. and averted more definitively in Star Trek: Discovery where astromycologist Lt. Paul Stamets and ship's physician Dr. Hugh Culber are in a relationship with each other.
StarDestroyer.net has four pages in its database about Federation culture... this trope dominates the comments, mostly in regards to the Federation's nebulous economics and highly conformist society. Debates about both topics are extremely common in fandom, not least because the various series are extremely vague about how the post-monetary economy works and because of the apparent lack of any contemporary pop culture (almost every character is a history buff with a preference for mid-20th Century or earlier subject matter). Site creator Mike Wong also wrote an essay that makes hay out of the '90s series' reliance on the Planet of Hats and the recurring trope that Half Human Hybrids are trapped between two cultures, arguing that it reinforces racial stereotyping and negative attitudes to interracial relationships.