No Blood Ties

A universe in which parents are not expected to raise their own offspring. As a consequence, few people value, or even acknowledge, parent/child relationships.

In this set up, loyalty to a society or community will probably be stressed over familial ties. The kids might not even know, or care, who their biological parents are. If they do, their relationship is one of polite deference or vague gratitude ("Thanks for making me exist"). There may be surrogates in the form of "foster parents", with parenting duties being delegated to a select group of trained and licensed guardians, but this is usually a creche-like setup where the foster carer has more children to tend to than is realistic. As a result, they don't have much time to give each individual child. It's no surprise then, that these caretakers don't tend to inspire much affection or loyalty (although they're almost certainly closer to the kids than their biological parents). Often, their role is basically to make sure the kid doesn't die while getting them to fend for themselves as much as possible. Alternatively, children may be integrated into a state-based boarded education system. If the civilization also sports a post-scarcity economy, children may be issued rights and independence sooner, and be allowed to determine their own habitats and social destinies.

There's a few ways this scenario can be played. If it's idealistic, and the system turns out well adjusted, independent children, then it's usually seen as a type of Author Appeal. Perhaps the author is suggesting that science, the good of the community and universal kinship should supercede bonds like family...but on the other hand, some observe that it may be a form of wish fulfilment, where you can ensure the continuation of your bloodline without getting "tied down" by the needs of a child.

Occasionally, the author might use this pragmatically. If they have adult characters running around and having adventures, a baby is going to get in the way. So the foster system ensures that the readers know that the character is a mature, responsible adult capable of procreation, but doesn't have to worry where the pram is going to go as they saddle up to defeat The Empire. Often, this character will be a parent when it suits them - they will be present for the child's major life events, revel in their baby's achievements, and acknowledge their relationship, but never actually change a nappy.

On the other end of the scale, this can be a major symptom of the Dystopia - especially if babies are raised from birth by machines, the military, corrupt Government puppets or in a factory-farm type environment. In this case, the decline of blood ties is related to the dehumanisation of the population, and they become little more than machines/weapons of war/brainwashed Mooks.

The Free-Love Future by necessity must have this attitude towards their kids, since any given person may have dozens of half-siblings, some of whom they might never have met, and the concept of marriage and the Nuclear Family is non-existent. Also worth noting is that surrogacy and Has Two Mommies/Daddies situations don't count, since they involve a sense of parental loyalty and being "exclusive" to a family. Families where parents (or children) work away from home and the other parent, or hired help, look after the children don't count either - they still identify as "belonging" to a family.

Examples of No Blood Ties include:

Anime and Manga

In Saint Beast, angels are described as being created through the love of God and have no man-woman distinction so blood relationships are impossible. They all grow up together in what is supposed to be a utopian community. Humans and gods, however, can reproduce normally resulting in the half-human half-angels Kira and Maya, sons of Lucifer, and Luca, Zeus' son.

Film

Logan's Run
- Has one of the main characters becoming severely annoyed that his friend even cares to wonder who his parents were. One scene shows the room of infants before they're taken off to be raised by robots.

Literature

Anne McCaffrey is keen on this trope.
- Damia of the Talents series was fostered, sent away by her father when her mother couldn't keep track of her. While this isn't mandatory in this universe, it's certainly not frowned upon.
- The Dragonriders of Pern use it to an even greater degree. F'nor remarks to himself that Manora "was only his mother" and gets annoyed when she expresses any concern or affection for him. Lessa and F'lar foster their son, Felessan (later F'lessan) and, after the young man is seriously injured, Lessa remarks that she was never particularly maternal. Manora reassures her that the work she did as Weyrwoman was more important than looking after her son, especially when the other women of the weyr were happy to do so. The Dragonriders' Free-Love Future is a major contributor to why there are no blood ties (although "Bloodlines" as a whole are considered very important as a mark of pedigree).
In The Giver, babies are produced by women whose job title was Birthmother (though the matter of how exactly these babies are conceived is never addressed) but raised in 'family units' composed of a man and a woman (matched up by the Elders), and one male and one female child.
- Given that everybody's sex drive is chemically inhibited (pills for "Stirrings"), it's safe to assume that the kids are fertilized in vitro.
The Green Martians in the first Barsoom book have their eggs taken by the elders, who chose the best to live. When they hatch, a randomly selected foster mother teaches the child to speak and a few other skills. John Carter sees this as hideously evil and the cause of much of their coldness. One Green Martian was conceived and reared in secret by her mother and knowing who her father is; she is much kinder than the rest. John Carter eventually reunites long suffering families after he leads the Green Martians in their conquest of the Red Martians.
In The Stand, community children started using "-Mom" as a sort of honorific, since they usually had multiple mother figures. (Kate-Mom, Nadine-Mom, etc.)
The Dispossessed by Ursula K. Le Guin.
Aldous Huxley's novel Brave New World. Babies are cloned, decanted and raised in Hatcheries and Conditioning Centres. Probably an inspiration for the Paranoia example.
True in large part for the Lilliputians of Gulliver's Travels.
Isaac Asimov's Robot Novel The Naked Sun. On the planet Solaria, children are raised by robots (overseen by a man or two) and have no contact with their parents. In "Robots of Dawn", the chidren on Aurora are mostly raised by professional educators, and it is highly unusual (though not impossible) for a person to raise or even know his children. One of the main characters tried that and it didn't end well.
- And in Foundation and Earth we see what has become of the Solarians. It's not pleasant. The main characters rescue a Solarian child from being killed because there aren't any recently-dead adults for her to replace. Still, at least Solaria is still inhabited by something close to humans, unlike Aurora and Melpomene. You might even say that the situation on Solaria is now better in some respects, since a person takes care and sees to his own child, instead of a centralized human farm. The Aesop seems to be that short-lived people who rely on manual labour are better than long-lived people who use robots. Which sits rather oddly with R. Daneel Olivaw being (albeit secretly) one of the crucial heroes of the Foundation series.
Asimov also has a story about a race of Starfish Aliens who are not just detached from their children - they are terribly disturbed by the thought of humans having blood ties. There is one female who knows who her child is, feels attached to him, but never reveals it to anyone, knowing there is a good chance she'll be killed, along with the child.
Theodora from the Ivory trilogy by Doris Egan was raised in a creche because the Pyrenese aren't into parenting too much.
Robert A. Heinlein's Hazel blows her stack at the thought of a child being raised outside the family, in a creche, when there is polygamous family where the child could be raised. Possibly justified by the fact that is exactly how she was raised giving her ample grounds to consider it less than ideal. Also the social conditions on Luna seem to have changed considerably in the decades between The Moon Is a Harsh Mistress and The Rolling Stones with a general shift from the exotic polygamous systems (caused by the drastic sexual imbalance) to a more conventional nuclear family.
This appears to be a major political debate in the third part of A Canticle for Leibowitz.
In the community portrayed in B.F. Skinner's Utopia, Walden Two, the children are raised by communal effort rather than by the parents. Biological parents' relationships with their children more like close friends, or like uncles and grandparents in modern Western society.
In Halo: Contact Harvest, it is mentioned that Sangheili are raised by maternal uncles instead of their actual fathers.
In K-PAX, prot (lower-case on purpose) says that children on his planet are raised by society as a whole, passing from family to family over the course of their childhood.
An extreme case is seen in The City And The Stars by Arthur C. Clark. In the city, Diaspar, new citizens are fabricated in near adult bodies by the Central Computer and then rather casually nurtured for twenty years by a randomly chosen 'Father' and 'Mother'. The only such 'family' we see is Alvin's and while Eriston and Etania are invariably described as 'kindly nonentities' Alvin clearly has a genuine affection for them and they apparently stand by him even though he's turned their world upside down.
The Race from Harry Turtledove's World War series work like this as a matter of necessity due to the fact that they have a mating season and lay eggs communally, so that not even the mothers know who their children are. An exception is made for the imperial family, as no females except the emperor's harem are allowed within his presence during the mating season to ensure that all his children can be accounted for (And he is the only one allowed to mate with them, to ensure that they're all his).

Live Action Television

The Peacekeepers in Farscape. Children born into the military (like Aeryn) are trained from infancy to be soldiers and to follow orders without question. Reproduction is assigned and parents have no role in raising their children. Even an attempt to contact one's child is punished severely, as shown with Aeryn's mom.

Aeryn:When you're born into military service the way I was, it's deemed best to not have any ties to anyone but your unit.
Bobby: No brothers or sisters? Aunts or uncles?
Aeryn: No.
Bobby: Didn't you miss that?
Aeryn: Only once I was exposed to it.

Tabletop Games

In Paranoia ~~mutant children~~ Junior Citizens ~~are popped out of clone tanks~~ are perfectly created via the generous wisdom of Friend Computer ~~and raised communally.~~ and raised collectively to the heartfelt benefit of all Alpha Complex.
The Clans in BattleTech use artificial insemination coupled with gene manipulation to create as-perfect-as-possible warriors. It's become so much of a tradition that "freebirth" has become the rudest insult they use.
The reptilian T'skrang of Earthdawn deposit their eggs in a communal creche, so knowing which hatchlings are your kids would require a lot of bookkeeping. They don't usually bother.

Western Animation

In Gargoyles, gargoyle children are raised communally by the adults of their "clan." Although blood ties exist, gargoyles do not distinguish (and usually don't even know the difference) between their own biological offspring and other children of the clan. When Elisa notes that Angela is clearly Goliath's daughter, he responds that she belongs to the entire family unit. Angela was raised by humans, however, and adopted many human values, so when she finds out that Goliath and Demona are her genetic parents, she expresses greater emotional attachment to them than to the other members of the former Clan Wyvern. Goliath, trying to resist the corruption of his traditional gargoyle values, intentionally avoids showing too much affection for Angela so that he doesn't appear to be showing favoritism toward his genetic offspring, until it's pointed out that she's the only child on his and Elisa's "world tour", and the youngest member of Clan Manhattan. (Demona, meanwhile, has her own psychotic obsession with Angela that doesn't really mesh well with Human or Gargoyle values.)
- This seems to be a cultural vs. personal. As a culture, the eggs are not bound to a family, rather to the clan (which clan is possible to change). On a personal level, Goliath and Demona both view Angela as their daughter and she sees them as her parents.
  - It's really pretty complex.
The Air Nomads of Avatar: The Last Airbender apparently raised their children in sex-segregated temples. Aang had a Parental Substitute in Monk Gyatso.
On Invader Zim, Irkens are grown in jars and enter training immediately after "birth." They nevertheless seem to have familial feelings, since Zim considers the "cold, unfeeling robot arm" that activated him as his parent.

Video Games

Your villagers under Black and White. Because of game mechanics, there's usually only one or two "breeders" in the village. The game, fortunately, didn't program in the problems with inbreeding.
The Charr race from Guild Wars and Guild Wars 2 live and breath this trope. Charr cubs only stay with their mothers for a very short period before being given over to Fahrars; educational camps where they will learn how to fight, unify and define their own social structures within their future warband, which are the only family that Charr have. Cubs have an awareness of their parents, but adults have no hand or interest in the training and growth of their offspring. Loyalty to the warband and the High Legion their warband belongs to supersedes any blood tie.

Web Comics

The Trolls in Homestuck never meet their parents. Genetic material is collected and grown in the eggs of a giant insect, and once the young Trolls grow out of the larval stage they are selected by a monster that they share the colour of their blood with. This monster becomes their 'Lusus Naturae' and raises them into adulthood. They can try to track down other Trolls that they share genes with by finding who had a matching sign, if they choose.