An ideally perfect place, especially in its social, political, and moral aspects.
Easy enough. Let's write one! First, you come up with a socially perfect place with a flawless political process. A "little" difficult, but you'll get there. Now figure out what "moral" means well enough to refine it to an absolute. Hey, it was tough, but you came through in the end.
Now get someone to agree with you.
Yeah. We can't help you with that part.
In fact, it is so much easier to get people to agree with what is wrong with a place that most social-commentary settings fall into the Dystopia category. When a brave author does attempt a Utopian setting it seems to come from a need to grind a particular axe. Thus we get libertarian/conservative/progressive utopias, religious utopias, communal utopias, and other philosophic one-note offerings, each with its own collection of people attesting they would rather die than live there. It helps that the word itself was created to mean such a place can't possibly exist because it's that good.
The downfall of a utopia in the main character's eyes will most likely be seeing the inevitable, thorough suppression of all individuality. How else could everybody get along all the time? Even in individualistic utopias, the supposedly rugged individualists who compose the perfect society have a suspicious tendency to agree on everything (or at least everything political) and act in similar ways. The end of violent conflict seems to require uniformity. Unless Rousseau Was Right but even then they need to have a similar morality. And now we're back where we started at the top of the article.
Obviously, when it comes to a television series, none of the main characters are going to be able to stay very long. It's hard to bring in conflict to drive a plot in a perfect world.
See also Perfect Pacifist People and Utopia Justifies the Means. Contrast with (of course) Dystopia. May run on Aesoptinum.
Arcadia - a place where people embrace the good old ways and live in wondrous simplicity.
Crystal Tokyo, the far future realm of Neo-Queen Serenity, in Sailor Moon.
Stellvia of the Universe depicts a rather realistic Utopia, wherein the humanity suffered 99% loss of population in mid 22nd century due to a freak cosmic cataclysm and was forced to unite as one, if they were to rebuild their civilization and survive. For the next 200 years, this Utopia was maintained by the threat of another cosmic catastrophe but as soon as danger was gone, it started falling apart. Even then, however, one could see just how difficult it is for most people to even imagine purposefully hurting others. Eventually humanity united again, against a new threat, and later, in their leap for the stars.
The original depictions of the Silver Surfer's homeworld of Zenna-La (the name being a variation on Shamgri-La) were decidedly utopian. Zenn-La was a very old, very high tech society that had long ago achieved world peace, where crime was virtually unknown, everyone was peaceful and learned, and where most human physical wants were easily met with technology. Its people had long ago explored great swathes of the universe... and having thus explored, they had come home again and stayed there. Norrin Radd, who would become the Surfer, found his world horribly boring, and resented the current generation (himself included) for reaping the benefits of their ancestors' labors which they themselves did nothing to earn. The 1990's animated series depicted a less isolated and introspective version of Zenn-La. In this version, the planet is famed throughout space for its spiritually enlightenment, and pilgrims come there to study the ways of peace. Even dissident Kree and Skrulls who want to find a way to end their millenia-long war. In both versions, they're defenseless when Galactus comes, until Norrin offers himself to the Planet Eater.
In one of the more peculiar utopias ever described, the skahs of With Strings Attached consider their world of 25+ years ago to be a utopia, since they're all adventure addicts and loved running around fighting the Tayhil and their monsters. Unfortunately for them, they slaughtered everything, and now they're all going crazy with boredom. It is, indeed, heavily ironic that what they now consider a Dystopia is actually, by Earth standards, far closer to utopia.
The world of the future in Bill And Teds Excellent Adventure is a utopia built on the music od Wyld Stallyns. George Carlin explains that right down the mini-golf scores, everything's just great. "Even the dirt... it's clean!"
The concept itself is much earlier than the name, going all the way back to Plato's dialogue The Republic, written in the fourth century B.C.E. Plato's Republic, besides being Older Than Feudalism, is the first of a long list of Utopias which most modern people would find terrifyingly totalitarian, with no private property and its caste system ruled absolutely by "philosopher kings". It also gave us the concept of the "noble lie", the mechanism Plato thought would hold it all together, namely people believing that they were born from the earth itself in their respective castes (to accomplish this, children would be taken away from their mothers and raised in State nurseries) and the gods or nature itself had ordained it that way. Since this was part of Hindu society for centuries, among the many other systems like this, it seems that it can work, if not perfectly.
Ironically, Aldous Huxley changed a few things about it that suddenly turned it into a utopia; that book is called Island.
Aldous Huxley wrote Brave New World as an interpretive utopia to show the problem with the concept of a utopia. The book arguably portrays a true utopia.
The Lord of the Rings has an often overlooked utopia in the form of "The Shire". The simple agrarian hobbits manage to live a leisurely lifestyle while remaining prosperous, and undoubtedly well fed. They have average lifespans well in excess of 100 years. They enjoy frequent celebrations and gift exchange. Their only armed force, Sheriffs, deal more with lost livestock then any real criminal behavior, and in fact in the whole history of the Shire there have been only four instances where the hobbits needed to muster any sort of military force, all were due to external threats. Apparently the Numenorians and their descendants found the hobbit's society particularly endearing as they've gone out of their way to defend the Shire from foreign invasion even after the fall of their own empire.
Le Guin's novel The Dispossessed is subtitled An Ambiguous Utopia, which nicely summarises the setting - Anarres is presented as a much less flawed world than ours, but it is still far from perfect. Le Guin puts down much of this to bureaucracy and the decay of the idealism that led to Anarres' founding in the first place.
Oz under the rule of Ozma is more or less a utopia; all problems come from either outside (particularly the Nome King) or from Oz's fringes.
The culture of the good guys in the first Chronicles of Thomas Covenant is a utopian one-with-nature form of Communism. This works, because everyone has a "health-sense" that makes them sensitive to their environment so that it actively hurts them if a neighbor/rock/potted plant is starving, ill, or mentally disturbed.
An idea mercilessly spoofed in the Stanislaw Lem short story "Altruizine" (from The Cyberiad). An idealistic alien robot clandestinely alters the human inhabitants of a planet to possess such a sense. After the ensuing carnage, the robot is found out and the humans show it their "gratitude" by crushing it into a cube and shooting it into space.
Heinlein sometimes sets his novels in utopias, to show how perfect life would be if we all followed his ideals. The moon society in The Moon is a Harsh Mistress is a Utopia based on brutality and easiness of death (which leads them to be all very polite to each other, and no one lacks food or shelter, there is no government to speak of...), and Starship Troopers' world is a Utopia in which only those who have completed a term of public service (including everything from medical testing to infrastructure maintenance to, oh yes, military service) can vote (their problems come from fighting aliens, and this is hinted that, eventually, it would be integrated into their society - the skinnies, not the bugs). The obvious problems with either of those societies are hand waved away.
In bizarre news, at least one actual nation had a member of Parliament introduce a bill to strip voting rights from those who don't complete national (mainly military) service. The measure was introduced (but not passed) because the place in question was extremely far from a utopia, and the MP putting the bill forward thought that since only a few special interest groups didn't already complete a form of national service, the Heinlein-thing would be a good way to limit the influence of those groups on politics.
Heinlein doesn't handwave the problems in either society. The anarchist utopia of Moon is plainly shown to be unstable in the long term. The protagonists consider it pleasant and desirable, but don't see it as sustainable. As for Starship Troopers, the internal problems and conflicts in the culture get a lot more mention than those of, say, The Federation in Star Trek — but the focus of the book is on (slightly naive) Johnny Rico's military service.
The Moon is a Harsh Mistress gets revisited a couple of generations later in the juvenile novel The Rolling Stones, where the moon now has a government and one of the protagonists is a smat mouthed, gun toting grandmother by the name of Hazel Stone, who's only concession to civilization is to load her sidearm with coughdrops (it's heavily implied that she keeps ammunition on her, though).
Heinlein was actually fond of deconstructing utopias. None of the societies he really portrays are utopian and the one in Starship Troopers is accepted by the masses in it because it works satisfactorily. Starship Troopers effectively deconstructs the utopia largely because of this and that the other methods of governing worked as well, though badly, and it is indicated that the society in the novel is just as faulty and came about largely because of the collapse of the previously existing systems leaving no apparent better alternative.
Gradually subverted in Strugatsky Brothers's Noon Universe. While the early installments portrayed the world of the 22nd Century as a more-or-less straight-forward Communist utopia, later novels began to subtly undermine this picture. Characters found themselves facing problems that clashed with their utopian mindset, the supposedly just government was revealed to be increasingly ruthless and duplicitous and the 22nd century scarcity-free society was shown to breed a class of bored intellectuals who went to extreme lengths to make themselves feel useful.
A more straight example is in works of I. Efremov: the "Andromeda Nebula", "Heart of Serpent" and "Hour of the Bull" all show us three consecutive times of a communist utopia. However there is a Fridge Logic subversion once you realize parallels between Earth' society and that of Tormance, the Dystopia society introduced in the third book.
In Efremov's case it's again more of a subversion. It is very heavily implied that this is the world After the End, and, just like in the Stellvia case, the people had to unite to have a chance to survive. In one of the As You Know historical lectures in the first novel a character describes centuries of coordinated effort to make Earth livable again. And still their society is full of conscious self-limitations and often seems surgically cold and somewhat hollow, as the emotional trauma still lingers almost a millennium past the cataclysm.
Ernest Callenbach's environmentalist utopia Ecotopia, in the novels Ecotopia and Ecotopia Emerginglinky.
The titular setting of Dinotopia is based around a peaceful coexistence between dinosaurs and humans. You know, except for the carnosaurs in the Rainy Basin. And that one guy nobody likes who rants about how Dinotopia doesn't mean dinosaur utopia - it really means "terrible place". He gets points for his Greek knowledge, but he's still a dork.
In the Robert Sheckley short story A Ticket to Tranai, the Earth-based protagonist has heard that the titular planet has no crime and no taxation. He finds out when he arrives that this is technically true, but only because there are no laws and the government employs muggers to take what it wants.
People in Stanislaw Lem's world in The Futurological Congress could live life as they liked by taking pills which changed reality. Later the hero discovers that everything he's seen has been hallucinated because the government was hiding — with more drugs — that Earth is overcrowded and freezing and everyone will die soon.
In his Observation on the Spot, another Ijon Tichy vehicle, Tichy visits Lusania — a country on the planet mentioned in one of his earlier adventures, where everyone lives in a seemingly perfect Utopia brought in by hypertech nanomachines. Half of the book is devoted to deconstruction of the folly of its creators — from the Tichy's standpoint he couldn't help to not notice glaring holes in the logic and workings of their society. And vice versa.
Ray Bradbury's The Toynbee Convector provides a man-made utopia in Earth's future. In the present, Craig Bennett Stiles announced on a live TV brodcast that he had invented and successfully tested the first functional Time Machine. While the machine shorted out on its maiden voyage, he did succeed in traveling 100 years into the future, procuring artifacts and video footage from the future and returning. He announced that within the next century, mankind would rise above its darker nature and abolish the evils that have plagued civilization; poverty, war, prejudice, hatred. We would wipe out all diseases, colonize the Solar System and live in perfect harmony with nature and with each other. 100 years later, that future has indeed come to pass, and a reporter locates Stiles, still alive at 130, on the day that Stiles' younger self is set to arrive in the future. In the resulting interview, Stiles reveals that he never actually traveled through time; the time machine, artifacts and video footage were all created by a special-effects team. He believed that, at the end of the 20th century, the world was careening toward self-destruction, and that mankind needed a vision of a better world, even if he had to invent that vision himself. He created the lie, and the world chose to make it the truth.
Live Action TV
Doctor Who had an episode actually called "Utopia", where it was a fabled respite from the horrors of a dying Universe. It constantly broadcast the message "Come to Utopia" on a loop, inspiring hope for anyone who was listening. The last humans spend the episode trying to reach it, finally setting off in a rocket by the end. However, there was no Utopia, or at least the last humans did not get to it. The Master, who was their leader in his previous, amnesiac form, finds them floating in space. They had converted themselves, using parts from the ship, into robotic Psychopathic Manchild cyborg kids who take joy in killing. The Master then brings the depressed psychotic masses to modern Earth.
The United Federation of Planets is said to be Gene Roddenberry's idea of 'Utopia' — no poverty, disease, or war exists on the Earth of the 24th century. Deep Space Nine, though, pokes some pretty big holes in that idealistic view, with terrorism, war, and a 'secret police' cabal that will do anything to ensure that everyone is safe and sound.
Given the replicator along with other high technologies (such as in medicine), there is some justification for the end of poverty and disease, but war obviously is still around. It would also make sense for humans to pull together after the Third World War and first contact with the Vulcans. Still, there are clear problems - for one, the implications of many technologies are barely touched upon - and it hardly justifies the Planet of Hats thing.
War does not exist internally within the Federation, it is a problem that the Federation tends to have with neighboring powers. Given the Federation's expansion and the availability of entire new planets for colonization, it is not surprising that many social issues are simply gone. No Federation race has to cram their entire population onto just one world if they do not want to. Thus common problems in future settings, such as over-populated mega-cities are just not present because anybody that wants more open space can move to a less densely populated colony.
In the pilot of Sliders, Quinn is visited by his double who says that he visited a Utopian world "Where no one was afraid".
Doctor Steel's stated goal is to remake the world into a Utopian Playland where having fun is the first priority.
Deconstructed in "Nothing But Flowers" by Talking Heads, where the singer describes an idyllic world... and is clearly bored.
Angelnetted worlds in Orion's Arm are essentially utopian. Within the angelnet you cannot be physically harmed, psychologically harmed, have your memeset (perception of reality) interfered with or have your rights violated. However the AI Gods are still the "iron fist in a velvet glove" so there isn't any real freedom, not that you'd ever know.
The problems with writing or even imagining actual utopias is discussed in thisLess Wrong article.
The Union of American Socialist Republics in the alternate history series Reds! is a deconstruction of much of the tropes of utopia. Is life in the UASR better? Perhaps. Is it very different? Absolutely. The author's seem to take a differentiating approach with this question. While communism is often seen as a utopian ideology, and the UASR has many of the facets of utopia (free love, classless society, great freedoms), this comes at a cost that people socialized to live in a capitalist, democratic republic might find quite uncomfortable, such as very great social pressures to participate in political and social life, and other duties that don't gel well with an individualistic society. The cultural and social values that developed over a century of tremendous divergence, revolution and the like are very much alien.
Futurama has a setting which has a distinct mix of utopian and dystopian themes.
Life on the Axiom in WALL-E is seemingly perfect, with everything done by robots, if you overlook the fact that humanity has devolved into fat, infantile couch potatoes.
What with the weight problem and the fact that everyone communicates via computer screens, you wonder how anyone on that ship managed to have babies. Unless the babies are genetically engineered or something.
Time Squad: A Cartoon Network series involving a time cop, a 21st century orphan, and a former robot diplomat who routinely back in time to set the changes of history on the right path. When not going time traveling, the three often hang out in their present time (the year 100,000,000 C.E.) on their spaceship near the Earth, which is referred in dialogue as a peaceful utopia where there are no longer any problems to solve (hence the reason for them making sure history stays on track, because otherwise their utopia could be ruined). All nations of the world have merged into one, and, according to the time cop, Tuddrussel, there are "no wars, no pollution, and bacon is good for your heart."
Ironically, the spaceship they live on and which they use to travel to the past is remarkably dystopic, as well as dark, outdated, and mostly unclean.