Newtypes from the Gundam series have superhuman spacial awareness and some empathic or predictive abilities. They are suspected/considered to be the next stage of humanity, a result of man's move into space.
Ghost in the Shell: Cybernetics are extremely common, with nearly everyone possessing at least a cyberbrain and some people going so far as to replace everything but their brains. Artificial intelligence is highly advanced but not quite human-level yet. And in the original manga and the films the major fuses with an emergent intelligence.
In the entirety of Blame!!, we do not see a single purely biological human. Everyone is heavily modified, be they cyborgs, human-descended androids, or gene-modded superhumans. The closest to "pure" human we get is Seu, and he's an eight-foot giant with enough enhancements to fight in hand-to-hand combat with advanced Silicon Life warriors, who has been reconstructed and had his personality restored from backup countless times. Most "normal" humans were exterminated by either the Silicon Creatures or the Safeguard, given the events of NOiSE,Blame!!'s prequel.
Puella Magi Madoka Magica presents a very disturbing take on this theme. Yes the girls do become supremely powerful, but in doing so their souls get ripped out of their body and placed inside a Soul Jar.
In Fullmetal Alchemist, humans have various degrees of self-enhancement. Some become walking armor, some get artificial limbs, and still others get transmuted into chimeras with new functional abilities. They have various degrees of acceptance of these transformations, as none of them was by choice. There are also the homunculi, who consider themselves an evolved form of humans.
Every superhero who was once a normal human. Inherently superhuman races do not count, unless they enhance themselves even further.
It's notable that only a small percentage of them gained their powers deliberately; usually it was a Freak Accident. This is arguably a necessary component of a superhero universe; if super-powers were easily reproducible, then the heroes themselves would stop being special.
Syndrome: "And when everyone's super, no one will be."
The corollary is that every Superhero who gave themselves superhuman abilities through technology which could work on other human beings and yet chose to keep it all to themselves (even via a You Are Not Ready justification) is a massive Jerk Ass who could be helping humanity on a global scale but chooses not to. Tony Stark springs to mind, but Reed Richards Is Useless too.
In-Universe, Tony has repeatedly tried to farm out parts of his armor tech to the government, and it invariably winds up getting used for evil and stupid purposes that make him regret the decision. As for Reed, he probably could find ways to empower someone if he wanted, but his own powers came from a standard-issue "freak accident."
Transmetropolitan: People buy "traits" in bulk ranging from cancer cures to implanted cellphones to alien genes. A few people upload their brains into clouds of nanobots called foglets.
In the appropriately named Transhuman by Jonathan Hickman medical advances make it possible to give people super powers. However there is a one power limit so everybody opts for Healing Factor.
Iron Man has been doing everything he can to transhumanize himself, ranging from cyborg parts to a Super Serum. Of course, it's debatable how much of this is symbolic of the lack of humanity in his behavior during the Civil War and its aftermath. Many fans theorize that the Extremis Formula caused a lot of his erratic, high-handed behavior, either by directly affecting his mind or just giving him a superiority complex.
Captain America would have been the first of an army of super-soldiers if the formula hadn't been lost immediately afterward. It's worth noting that the existence of a few other, far less successful super-soldiers like USAgent stand as proof that it's not just Cap's powers that make him Captain America, it's his personality.
Friendship Is Optimal revolves around humans uploading to Equestria. While Immortality comes as a standard part of the package, an uploaded human can also have their mental abilities significantly increased if they desire.
Blade Runner: The eponymous character hunts down renegade artificial humans.
Repo! The Genetic Opera has nearly everyone using artificial organs produced by GeneCo, and cosmetic surgery is even more common thanks to an addictive painkiller.
Captain America: The First Avenger: Bonus points for explicitly portraying the morality and 'heart' of the Super Soldier as being just as important as physical (and possibly mental) improvements. There's no Psycho Serum either - they both got the same Super Serum, but Schmidt was impatient.
Arguably, the protagonists in the Tetsuo: The Iron Man films. Sure, they become grotesque walking lumps of scrap metal, but as the films go on, they can sprout guns from their bodies, become giant tank things and crawl on walls.
Star Trek: Into Darkness: Notable because of the franchise's attitude towards this subject in the past that a heavily-augmented human (named 0718) appears as a member of the Enterprise crew. Possibly as a minor counterexample to Khan, since he doesn't have any major significance beyond calling out a couple of lines.
Live Action TV
The crew of Andromeda includes three genetically enhanced humans, a cyborg, and an android who is a semi-autonomous avatar of the ship herself.
A more fantastic version could also be applied to Q and the rest of the Continuum.
Julian Bashir from Deep Space Nine is transhuman thanks to his genetic enhancement. He puts it to good use. Other genetically enhanced people, however, tend to end up having various drawbacks, including mental instability or evil-inducing levels of ambition.
Though, due to genetic modification of this type being illegal, it's carried out primarily on children who are already "damaged" by doctors with restricted resources and no support. The Star Trek universe is kept from full-scale transhumanism primarily by editorial dictates.
Khan Noonien Singh and his followers had genius-level intelligence and five times the strength of a normal man.
Also, the Vorta, who were uplifted from ape-like beings into what they are now by the Changelings. The other main Dominion race, the Jem'Hadar, are also genetically tailored by the Changelings into loyal super-soldiers.
The Changelings themselves were once "solid" humanoids, and it's implied they reached their current form through some kind of technological means.
The Organians (original series) stated that once they were as human as Kirk and his crew, but had evolved into creatures of pure thought and energy.
This is at least implied to be the origin of most Energy Beings in the Trek verse, like the Companion, Sargon, the Zetars, (possibly the Bajoran Prophets in a Timey-Wimey Ball manner), etc.; probably even the Q, since they seem to think humans are on the path to becoming like them.
Gary Mitchell and Dr Elizabeth Dehner both acquired psi-powers from the galactic energy barrier - within a few hours Mitchell could read the entire library of the Enterprise and could telekinese, create small objects, and project energy from his fingers, with Dr Dehner just a short way behind him. It's impossible to be sure, but they might have hit Q power levels a few days later if they had lived. Unfortunately, Gary becomes a psychopath. Spock believes Transhuman Treachery in such a situation to be inevitable, as the transformed would come to view mere humans as a petty annoyance.
In one ST novel, it was Q, beaten in a fight by Trelane, reduced to mere essence, and tossed back in time a million or so years, that provided the power to Mitchell and Dehner.
This is half of the origin story of the original Kamen Rider: Takeshi Hongo is kidnapped by the terrorist organization Shocker, and upgraded and brainwashed into one of their cyborg super soldiers. The other half? He's a Phlebotinum Rebel, and uses his new powers to fight against his "creators".
The trope happened to every other Showa-era Rider as well, and you can make an argument for some of the Heisei Riders. (Ishinomori had a thing for the trope, in the sense of how one can find or lose their humanity through it.)
Choujuu Sentai Liveman has some fun with this trope - all the members of Volt manage to play out this trope in different ways, with the exception of Guardroid Gash. And all of them die less than pleasantly for it, save one.
Almost everyone in Duumvirate is either born transhuman, becomes transhuman, or desperately wants to be transhuman. When your regeneratively immortal friends can play Bullet Hell games at maximum difficulty without breaking a sweat, and dodge actual bullets for that matter, you tend to get a deep appreciation for genetic superiority.
In Nietzsche's Thus Spake Zarathustra, Zarathustra preaches that mankind's future lies into the ‹bermensch. A form of spiritual/mental transcendence into godhood.
Beggars in Spain is about the rise of a new breed of transhuman, the "Sleepless".
Childhoods End: Aliens guide humanity into ascending into a galactic superconsciousness.
Oryx and Crake: Crake designs a new species of human who mature quickly, eat only plants, turn blue when they go into heat, can heal wounds by purring, and keel over at the age of thirty. It's made pretty clear that he was insane.
The Quantum Thief. Notably the society of Oubliette on Mars is resistant to most transhuman technologies, being built on the ideals of privacy and individuality, yet from the reader's perspective it's still filled to the brim with transhuman technology designed to ensure this state of affairs. For starters the citizens all have a specialized privacy sensory organ called Gevulot through which the majority of their communication takes place.
Many of Robert Reed's novels and short stories deal with transhumanism and effective immortality
The Great Ship universe goes into a bit more depth. So long as the brain is intact, the individual can be revived. And in this case, "intact" is pretty broad. One man shoots himself in the head to stow away on a ship (life signs detectors can't find you if you're dead!), and the captain is so impressed that she makes him a lieutenant. Humanity has had some pretty significant biological changes, as well - every human has artificial constructs in their bloodstream called "emergency genes" which make them absurdly durable, and will regenerate tissue and limbs if given enough mass.
The Winemaster had a significant portion of the United States population download their brains into tiny, fantastically fast robotic bodies, who are isolated into enclaves which use magnetic fields to protect their fragile minds from heavy particles and radiation. By the time the story takes place, most of the posthumans were never even human to begin with - instead being the artificially created "children" of the original posthumans.
John Varley's Eight Worlds setting is filled with transhumanism. Even though human genetic experimentation is technically illegal there's always surgery, symbionts, cybernetics and nanotechnology so it's not unusual for people to modify their bodies (sometimes radically) to suit a specific environment, fad, fetish, or job. While the people who go for the most radical physical modifications tend to be professional spacers (who tend to discard things like legs and feet that are not very useful in zero gravity) most people are so cyberized the lunar central computer admits to tapping the unused portions of their brains for additional processing power.
The Mesan Alignment has been practicing the biological form of this in secret for quite some time and believe they should share it with the rest of the galaxy... by force.
There's also a brief mention in on of the early books that there are a handful of planets in the galaxy where cybernetic transhumanism is a common practice but they're fairly isolated incidents.
At the less radical end, Honor herself and a number of other characters are genetically engineered for living on high-gravity worlds. And the relatively recently-introduced prolong treatments have vastly expanded the life expectancy of anyone who can get them. It isn't actually known whether later-generation prolong recipients will ever experience old age. In wealthy star nations, the treatment is nearly universal.
More extreme human bioengineering is avoided as backlash to the Super Soldiers used in the last war fought on Earth. Some of their descendants are still around.
Discussed towards the end of Vernor Vinge's novella "True Names", when Slip and Ery finally meet face-to-face. Not too surprising, since Vinge is generally credited with popularizing the idea of The Singularity.
In Star Trek: Ex Machina, it's revealed that Will Decker was essentially a 23rd century transhumanist, with a personal spirituality deeply concerned with "unexplored potentials of the human mind". His particular dream was an All Your Powers Combined scenario whereby different species could transcend their limits by uniting their psyches and spiritual essence. This, he hoped, would let them sense or reach new levels of existence. For this reason, he was strongly drawn to species with telepathic abilities.
In the Takeshi Kovacs series, all humans have their identities backed up in "cortical stacks" that can be transferred to any body (aka "sleeve") they wish. Many sleeves are artificially created to have a range of nonhuman enhancements. They can also upload themselves into non-organic robot bodies or simply into computer programs.
There are several experimental engineered human species in Black Man... the bonobos, designed to be sexy and submissive (and exclusively female), hibernoids who go from frenzied sleepness workaholism to extended hibernation sleep (useful on a slow-travelling spacecraft) and of course the 'Variant Thirteens', scary pre-civilisation throwbacks who are incredible badasses combined with a complete disregard for hierarchial authority structures and no need to feel a sense of belonging.
The goal and ideal of the (admittedly loopy) narrator of Jonathan Coulton's "The Future Soon".
'Cause it's gonna be the future soon, I won't always be this way/As the things that make me weak and strange get engineered away...
Also, the Elan Race in 3.5e's Expanded Psionics Handbook and the bloodline feat chain of the same name in 4e D&D's Psionic Power is essentially this: humans who underwent body modification to turn themselves into an immortal being powered by thought.
The Dragon Disciple Prestige Class is a magic user who taps into the latent power of a Draconic ancestor to take a Dragon-like form.
In Pathfinder, this is a theme of Sorcerers. As they advance in power, the supernatural bloodlines that give them their natural magic also begin transforming their bodies in subtle, then overt ways.
GURPS:Transhuman Space has multiple levels of human genetic modification, artificial humans, artificial intelligence, nanosymbionts, brain uploading (albeit one-way) and uplifted animals. Very few cybernetics though, they're considered outdated.
In Shadowrun, many people have some degree of mechanical alteration - cybereyes are the most common bit of cyberware in the world. Mages on the other hand can't use them with out messing up their Essence/magic. Also, the metahuman races are humans who have been altered by the return of magic.
Eclipse Phase specifically states that its big underlying theme is trans-humanism and exploring both the technological and psychological aspects of it. All the rule books use transhumanity instead of 'humanity' and wants you thinking about it.
Several Exalted types are quite literally transhuman. The Alchemicals start as cyborgs with human souls, and eventually turn into giant robots and even living cities as their permanent Essence rating increases. The Infernals have the ability to become like their Yozi patrons, the many-souled, world-like beings that first made the world. You've even got cases among the other Exalted, like the First Age Solar Queen Ktula, who experimented with her body so much that a bunch of her Charms shut down because her Exaltation no longer recognized her as human.
Abyssals too. Except that rather than become something more than human, they become something less - something hollow and malignant, a walking conduit to Oblivion. The ultimate destiny of the Abyssals could be Deathlords Mark Two - or something greater and more terrible than even the Deathlords can imagine. Or, y'know, they could kick the Void in the face and powerload hope and light into their Shards until they can achieve redemption and become Solars. One of the nice things about Exalted is that there's always a choice.
Absolutely all Alchemicals are transhumans of the cyborg variety. In fact, they have special meter that indicates how far removed they are from the thought processes of normal humans, called Clarity. They have charms with cyberpunk names such as Man-Machine Interface and God-Machine Interface, which achieves what sorcery does by hacking reality itself. And then there is Voidtech, which is a path of organic transhumanism...
Magic The Gathering has New Phyrexia, where normal organisms get transformed into more dangerous Phyrexian ones by the oil and Phyrexian bioengineering, while native Phyrexians are born as naked "newts" that can be perfected into a number of general templates based on role through surgery.
It also applies to old Phyrexia; the process of Phyresis in The Thran is very akin to transhumanism, since Yawgmoth not only cures the afflicted of their phthisis, but also transforms them into war machines and then explains that they are the future heroes of the Thran (heh).
Urza also dabbled in transhumanism with his genetic experimentation and the creation of the Metathran.
In Strike Legion, transhumanism is ubiquitous. The average human in either the Imperium or the Star Republic is already genetically enhanced to the point that they make modern humanity look like degenerate apes. This is before factoring in extensive bio-augmentation, cybernetic implants, and nanotech enhancements which are commercially available to civilians and military. And that is before one gets into the Imperium's countless supersoldier programs (cybernetic modification, genetic modification, extradimensional modification, genetically-enhanced Reality Warper powers....) and the Republic's LegionProcess.
Mass Effect has humans that are enhanced both through gene therapy and cybernetic enhancements. Furthermore, exposure to the substance "Element Zero" has caused a small percentage of the population, known as biotics, to gain powerful telekinetic abilities. To make practical use of their abilities, biotics require a piece of wetware to regulate their nervous system called a "biotic amplifier". The amps themselves are modular, the sockets implanted in the biotic's head are not so much.
In the sequel, Shepard's resurrection necessitated "Bio-synthetic fusion" where Shepard was given extensive cybernetic implants wired throughout their body that serves to reinforce their skeletal structure, enhance strength, improve organ function and supplement their central nervous system. Project Overlord reveals that Shepard is just about machine enough to briefly be taken over by the Overlord "Virus".
All organic beings become transhuman in the "Synthetic" ending of Mass Effect 3.
It also applies to the Geth in the same game, if Commander Shepard so chooses, as each Geth program becomes a sentient entity in and of itself.
Curiously, this trope is Played With by also balancing it against No Transhumanism Allowed. Out of concerns that species might lose their biological uniqueness, genetic enhancements are regulated by interstellar accords. The general rule of thumb about this is that enhancing existing traits through genetic modification is okay, but adding new traits that the original would never naturally possess is forbidden. So for example, a human could be made smarter, stronger, and quicker, but could not be given a tail or the ability to digest cellulose. This seems to only apply to genetics though (as those are passed down to children.) Cybernetics (which are not) seem to be acceptable.
The Advent from Sins of a Solar Empire, in contrast to the No Transhumanism Allowed Traders. Part of the reason why the Traders exiled them in the first place. The alien race present in the game, the Vasari, are as of their in-game state, also technologically improved to varying degrees from their biological baseline.
Terran Ghosts from StarCraft and StarCraft II both thanks to their inherent psychic abilities and the technology and training that helps them harness it (and keep it under control). Also, Protoss Dragoons, Immortals and Stalkers are mildly Trans-Protoss by virtue of their mechanical bodies.
The goal of the Zerg Overmind was to assimilate new races, becoming more Trans-Zerg each time. The Overmind's finest creation was Kerrigan, the first Zerg to wield psionic powers.
The driving background element for the entire Deus Ex series:
Transhumanism is a major theme in Deus Ex: Human Revolution. You've got people in support of it, people against it, lots of reasons for both pitted against each other in several debate scenes, and Adam Jensen himself has lots of cybernetic upgrades, also called augmentations.
In Deus Ex itself, heavily augmented humans are commonplace. The primary motivation of the villains seems to be to establish themselves as posthuman overlords, ascending to godhood while ruling over a population of unaugmented minions.
Deus Ex: Invisible War portrays either a pseudo-religious backlash against all transhuman technology, the peaceful integration of trans- and normal humans, or the complete (but involuntary) ascension of the species to a new plane, depending on player choices.
There are also the Jove. The Jove used to be human, but have biologically modified their bodies to such an extent that they can't really be considered human anymore.
Alice Margatroid from Touhou used to be human, but transformed into a magician Youkai.
Byakuren Hijiri is very big in surpassing human limitation, and got banished to the aforementioned Pandemonium by humans who weren't pleased with her becoming a youkai. She has an arsenal of body-enhancing spells, for beauty and for combat. One of her spellcard is titled Superhuman Byakuren Hijiri.
Ironically, Byakuren's major ideological rival Toyosatomimi no Miko is also a big proponent of transhumanism, claiming that her own transformation into a hermit was "overcoming her humanity". The main difference between them is whether they would consider being a youkai acceptable.
It also seems to be what version of the virus, Fawkes and the DC mutants were made with an early version. The Master's army was the "newest" resulting is most being at least human level mentally. The Enclave's mutants updated the Master's but due to their racist views they designed it to make them dumb.
The SPARTANs in Halo, although in the games it's portrayed more as soldiers wearing Powered Armor. The EU goes a great deal further into explaining that they biologically and cybernetically enhanced the bejeezus out of them before putting them into their really fancy armored suits. As such, the in-game physical strength and stamina of the SPARTANs comes from a combination of their biological enhancements and their powersuits.
In Crysis, this is the ultimate goal of Jacob Hargreave. He has been working for more than a century to prepare mankind for war with the Ceph, using their own stolen technology to enhance human technology, and it culminates in the Nanosuits, which are hyper-advanced Powered Armor designed to turn their wearers into "post-human warriors." They go so far as to literally replace entire organs, co-opt brain functions, and generally turn their wearers into full-on nanotech cyborg supersoldiers, and are capable of sustaining a person even after death, and on top of that, they contain internal machinery and advanced computers that can sample, analyze, and adapt to Ceph environmental weapons.
In Metroid, protagonist Samus Aran has had durability, agility, strength, poison resistance, and parasite resistance enhanced via addition of alien DNA, and has been shown to have her Powered Armor literally attached to her nervous system, to the point where she can make it suddenly appear by concentrating (although taking it off again is a bit more complicated, as the doctors found out in Metroid: Fusion). Its entirely possible she's also got a menagerie of superpowers in her DNA from Fusion, but its never made quite clear if those powers are DNA-based or not (and the issue is debated heatedly).
All of the demigods in Asura's Wrath are transhuman, as well as descended from transhuman beings.
Final Fantasy XIII and its trilogy have Human's that are transformed into L'cie, making them stronger and giving them the ability to use Magic. After the end of XIII, some people begin to learn to use Magic normally without becoming a L'cie, and by the time Noel Kreiss is born 700 years in the future this is the norm for everyone.
Taken even further with the Main Protagonist, Lightning. In XIII she goes from a Human to a L'cie. After XIII she goes from a L'cie to a human possessing the magic of a L'cie (according to "The Fragments After"). Just before the events of XIII-2, she goes from a human possessing the magic of a L'cie to being given immense power by the Goddess Etro and being called a "Warrior Goddess" at one point and having the manual state she's "something more than human... almost a Goddess herself". During Lightning Returns, she will now serve as "The Soul Liberator" and has been said to be even more powerful than before. Now, she even begins to question whether or not she's even human anymore at this point.
The ethical ramifications of transhuman engineering are touched upon in XCOM: Enemy Unknown once you come across the cybernetically-altered aliens, particularly the Floaters, who are essentially Mutons whose lower bodies have been hacked off and have had jet engines integrated into their backs. Dr. Shen, in particular, is horrified by the idea, and even moreso that that humanity might end up following the aliens' path. He also expresses both apprehension and awe when XCOM figures out how to develop Psychic Powers. Goes even further with the Enemy Within expansion, where the player is able to apply the aliens' own "Meld" technology with their soldiers, enabling them to create genetically-boosted and/or cybernetically-enhanced supersoldiers piloting Mini Mecha.
Kimiko of Dresden Codak is all for transhumanism. In the Hob storyline, an alternate universe version of her didn't do a terribly good job of carrying humanity through its Singularity and apparently came to a sticky end. The human remnant of that reality did make the step into trans-humanity in the end though.
Schlock Mercenary is loaded with the stuff. Cyborgs, nanomachine-based boosts, genetically engineered sophonts (including uplifted animals), and that's just for humans. Interestingly Schlock Mercenary approaches the the concept from the other side as well. Haban II and The Fleetmind/Petey started out as pure AIs residing in computer systems but both have since have partially migrated into organic vessels. Haban started as the AI half of the human/AI team of DoytHaban but after his gate clone suffered a severe head injury, functionally killing Doyt, leaving one version with Haban as the sole intelligence. Petey on the other hand created multiple 'blank' clones and use hypernode communicators to wire them into the Fleetmind Gestalt to act as physical representatives.
Note that Petey did this specifically to loophole his creators' version of the Second Law of Robotics, by giving himself orders from an Ob'enn body.
Among The Chosen most of the cast fits into one type or another, though there are a few unmodified humans.
Very deeply explored in Orion's Arm, to the point that baselines (regular non-modified humans) are something of an endangered species by 10600 AT. It's also not limited to humans; several xenosophont species have also embraced self-enhancement, and animals both terragen and alien have been provolved to sophonce.
As noted above, any Religion that offers an afterlife, including Christianity, are the obvious Ur Examples of Transhumanism. The Moral Guardians may want to deny it, but their Central Dogma is that the humans that follow them would eventually abandon their weak "sinful" bodies and Ascend to a Higher Plane of Existence free from sin or death. A lot of Pauline, Gnostic and Theological literature encourages despising the flesh in favour of the Transhuman ideal in Heaven. One could even say that the Moral Guardians themselves are doing enough efforts encouraging and justifying Transhumanism with their constant propaganda about how the flesh is sinful.
All of this seems to be forgetting that every religion's 'ascension' has nothing to do with being alive at that point. The concept is entirely spiritual.
The Transhumanist movement. There are no transhumans yet, of course, but they would like to promote research into science and technology that would make it possible.
People who have undergone gene therapy or use electronic prostheses, cochlear implants, and the like are the start of what the Transhumanism movement hopes to accomplish. These bits of tech are examples of human enhancement technology that is traditionally used for people with disabilities to bring them to being roughly the same as a perfectly healthy human, and the same technologies could conceivably be used to elevate anybody to have greater-than-human attributes.
The US military is developing an eye implant code-named "Luke's Binoculars", which is designed to augment a person's own ability to distinguish Friend or Foe by amplifying certain brain signals they should be paying more attention to.
Cellphone and key-chip implants.
Nootropics. Basically brain boosting pills. They've gotten better in the last couple of decades. The good ones don't necessarily push you into superhuman territory so much as they allow you to function closer to your optimal level with greater consistency and, in some cases, in spite of age.
Also of note are smartphones. Small computers that are capable of doing pretty much anything their desktop counterparts can do, with their owner at all times (or at least as long as their owner chooses). The only difference between the characters in Ghost in the Shell and a person with a smart phone is that the former has a more seamless interface than the latter. It may be only a matter of time before they becomes a luxury implant.
Man-machine interface exists to let users tap into computing powers without becoming cyborg themselves.