Alternate World fantasy involves different worlds hidden within or parallel to our own. In past times these could be found in a mysterious country, as in Johnathan Swift's novel Gulliver's Travels. With the Earth explored, some were envisioned inside a mirror, as with Lewis Carroll's novel Through the Looking Glass. Others 'distill' whole fictional libraries, as with John Myers Myers' novel Silverlock. In a scientific era, often these worlds are in a parallel cosmos, as depicted in Roger Zelazny's "Amber" series.
Bangsian fantasy takes its name from a 19th century author named John Bangs. This subgenre deals all or mostly with the afterlife. Early legends speak of Hades, and it's been going strong ever since. A modern example is Philip Jose Farmer's "Riverworld" series. Though marketed as literary fiction, with its Heaven-dwelling narrator, Alice Sebold's novel The Lovely Bones fits this category.
Contemporary is a subgenre which posits that magical creatures are hidden amongst us. These tales are set in modern times, and deceptively familiar situations. Neil Gaiman's novel Neverwhere depicts a vast (yet hidden) magical underground London. Mercedes Lackey's "Diana Tregarde" novels bring realistic magic to Dallas and small town Oklahoma.
Court Intrigue is a subgenre set in royal castles, whether historical (but with magic), or in some recognizable alternate world. George R. R. Martin's novel "A Song of Fire and Ice" and its sequels (plus the HBO version A Game of Thrones) are good examples.
Heroic fantasy centers on a conquering hero, or band of heroes; yet it often turns the genre's heroic trope on its head, with forgivable villains and deeply flawed protagonists. Stephen R. Donaldson's epic "Chronicles of Thomas Covenant" series fits the bill perfectly.
High or Epic fantasy is, for many readers, the heart and essence of the genre. Entire worlds are created, with long histories and vivid lifestyles, and a large cast of characters. Tolkien's The Lord of the Rings utterly dominates this subgenre. Elizabeth Moon's five "Paksenarrion/Gird" novels (plus some brand-new sequels) are excellent examples. (Hand-drawn maps, which show the landscape and competing realms, are essential.)
Historical fantasy is the genre's answer to historical fiction. A specific period from Earth's history becomes the setting, but with fantastic elements blended in. Gene Wolfe's dreamlike novel Soldier of the Mist and Guy Gavriel Kay's novel Tigana are two fine examples.
Juvenile fantasy is a vast descriptive category, overlapping with the 'children's' and 'young adult' genres, which has stories written for a younger audience. Tolkien's The Hobbit is a stellar example, as are L. Frank Baum's "Oz" books. Joy Chant's novel Red Moon and Black Mountain is another.
Medieval fantasy is defined by its name, as this subgenre's tales are set in that period, in between the ancient or Arthurian worlds and the modern industrial era. They will feature knights and knaves, often together with sorcerers and dragons. (Many fantasy subgenres, set on Earth or elsewhere, have a 'pseudomedieval' setting. That is: ox carts, tavern wenches, and swords; but no automobiles, stock brokers, or firearms.)
Quest fantasies involve just that. It's a descriptive category, in which the protagonist is involved in some perilous all-consuming quest. In Peter Beagle's novelette Two Hearts, nine-year-old Sooz sets off alone to free her village from a murderous gryphon. Terry Goodkind's novel Wizard's First Rule is another example.
Aliens infuse this subgenre with relentless troublemaking. Overlapping with 'science fiction,' the source of terror is another planet, whose inhabitants are encountered there, or travel to our Earth, if not both. The "Alien" franchise (featuring Sigourney Weaver) leads this charge. Scott Sigler's novel Infected is a recent example, among many. In M. Night Shyamalan's movie Signs, mysterious rural visitors are revealed to be (somewhat improbable) aliens.
Dark Romance is a relatively new subgenre which mixes supernatural elements (Vampires, Werewolves etc...) with romance. The most obvious example is the "Sookie Stackhouse" series by "Charlene Harris".
Humorous horror is fairly common, and its macabre elements are often understated--or exaggerated into parody. The old comic strip and TV show The Addams Family are familiar examples. The anthology Blood Lite from Kevin J. Anderson is a recent contribution to this subgenre.
Lovecraftian (Cthulhu mythos, etc.). These subgenres are rooted in the pioneering fiction of H. P. Lovecraft. The originals and newer works have a distinct style, with florid prose and an overwhelming pessimism. (They overlap with 'science fiction,' as his In the Mountains of Madness was first serialized in that genre's magazine Astounding.)
Mind Control horror exploits this particular fear. The method may be sorcerous or technological, but the victims are compelled to act against their will and better natures--often while fully aware of what's happening. False Memory, by Dean Koontz, is a popular example. Curt Siodmak's novel Donovan's Brain is an early example of invasive medical technology gone awry.
Zombies are popular enough to warrant special mention. For example, Richard Matheson's 1954 novel I Am Legend and its several film versions. Others, such as Edgar Wright's film Shaun of the Dead, contain humorous elements. A key element here is that the zombies are often more environment than antagonist
Alien Invasion stories are self-explanatory. The target is usually, but not always, our Earth. The classic of this subgenre is H. G. Wells' pioneering 1898 novel War of the Worlds, followed by Orson Welles' 1938 radio version. Larry Niven and Jerry Pournelle's novel Footfall is a well-thought-out example. The film Independence Day, by Roland Emmerich, has become a cultural milestone. (Most--but not all--of this subgenre's tales depict an eventual human triumph.)
Alternate Histories depict might-have-beens, if one or more crucial situations had been resolved differently. Common themes are: what if the South had won the Civil War, or Germany won World War Two? The grandmaster of this subgenre is Harry Turtledove. Another example is Philip K. Dick's novel The Man in the High Castle.
Bigger Than Worlds is a subgenre well-described by its name. Vast artificial megastructures are the setting for these stories; almost characters in themselves. Olaf Stapledon's 1937 novel Star Maker is probably the first such tale, with a star-englobing construct of a type later known as a Dyson Sphere. Larry Niven's 1970 novel Ringworld introduced that carefully thought-out habitable structure. This subgenre's largest imagined construct (at tens of millions of light years across) is perhaps Bolder's Ring, found in Stephen Baxter's "Xeelee" novels.
Clerical subgenre tales involve an organized priesthood, such as a religious order, of any human or alien religion. Set on Earth, Walter Miller's novel A Canticle for Leibowitz chronicles one sincere and long-lived order. Frank Herbert's Bene Gesserit (in his "Dune" franchise) dominates human history, yet without profound expressions of individual faith.
Communalness is a specialized term and subgenre, involving a human future with relationships and communities 'boosted' into enhanced consciousness by cybernetic or other means. The namesake town in Frank Herbert's novel The Santaroga Barrier has achieved a kind of drug-induced unity. The disciples of V. M. Smith in Robert A. Heinlein's Stranger in a Strange Land achieve this (along with impressive powers) through learning to speak Martian.
Cosy Catastrophe is a type of postapocalyptic tale, usually set on Earth, in which an isolated group of survivors sets about rebuilding a new civilization according to their own particular ideas. (As with the 'cosy mystery' subgenre, unjust death has occurred, but the characters don't get too rattled about it.) The founding example is probably Mary Shelley's less-well-known novel The Last Man. Another is John Wyndham's novel The Day of the Triffids, later filmed by Steve Sekely.
Cyberpunk is a term that's expanded well beyond the SF community and into popular culture. (It's also spawned a host of other "-punk" subgenres.) These tales are typically set on Earth, and involve a hacker immersed in a cyber-world, interacting (both on line and physically) with similar people. Often they're modified to 'jack' their brain directly into cyberspace. The founding tome is William Gibson's novel Neuromancer (It may be an unwritten law that all such tales must involve preening characters gathered in a flashy night club.) Technology use is a rare skill, rather than the norm.
Dying Astronuat tales got a boost from the real-life events of the Apollo 13 mission, as depicted in the movie from Ron Howard. With the laws of physics precluding any possible (outside) rescue, these stories can range from tragic to poignant to heroic. In Alfred Bester's novel The Stars My Destination, a man abandoned on a derelict spaceship figures out a way to survive. In "Wonders of the Universe," a short story by German author Andreas Eschbach, a marooned woman dies gracefully on frozen Europa.
Dying Earth SF tales show the death of the Earth as slower than from an apocalypse, and it can be due to any cause, including natural. A haunting vision of this appears in the far-future chapters of H. G. Wells' novel The Time Machine. (Including a 'lost' chapter about a biologically decrepit humanity, originally serialized but not included in the novel and film versions.) Isaac Asimov's novel Pebble in the Sky is another example.
Dystopian (crowded world, gilded cage, jaded society, theocracy, etc.) The opposite of Utopian, these horrid societies are all too easy to imagine. In most such tales, the protagonist seeks to better his-or-her own life, if not to liberate the entire society.
Generation Ship stories are set aboard that type of spacecraft. Often those ships are so large, and the voyage so long, that (most or all of) its inhabitants consider other worlds to be the stuff of legend. The subgenre was pioneered by J. D. Bernal, with his 1929 novel The World, The Flesh, & The Devil. A popular example is Robert A. Heinlein's novel Orphans of the Sky. Another is the original Star Trek episode "For the World is Hollow and I Have Touched the Sky."
Gothic SF is an overlapping subgenre that slants toward the macabre, and deeply atmospheric settings, but not outright horror. ('Atmospheric' in a literary and cultural, not climatological, sense.) Mary Shelley's Frankenstein is often cited as the first such novel. Algis Budry's novel Rogue Moon sets a determined pair against a deadly lunar enigma. Arthur C. Clarke's short story "A Walk in the Dark" is another example.
Hollow Earth tales are just that, set within a putatively hollow (or at least honeycombed) planet Earth. The flagship of this subgenre is Jules Verne's novel Journey to the Center of the Earth. Michael Flynn's novella "Where the Winds Are All Asleep" is a modern homage. A popular variant is the aquatic-cavern-filled planet Naboo in the "Star Wars" franchise.
Lost Worlds (mysterious islands) is one of the oldest SF varieties. Sir Arthur Conan Doyle's novel The Lost World, based upon South America's then-mysterious 'tepui' plateaus, lent its very name to this subgenre. Later novels 'discover' isolated valleys in central Asia or elsewhere.
Military is a huge subgenre, with its own specialized publications. Soldiers and warfare are central to these stories. Some are near-future, and depict humans fighting each other. Others span star systems and even whole galaxies, with vast ongoing conflicts with aliens. David Drake and Elizabeth Moon are masters of this field, while Joe Haldman's novel The Forever War will soon be filmed. David Feintuch's "Hope" novels essentially translate the 19th century's British Royal Navy into outer space. (Usually the humans and aliens are closely matched, lest it become a rather short "Bambi vs. Godzilla" type story.)
Parallel Universe SF is similar to the Multiverse subgenre. In this case, the other universe(s) can be very strange, with differing physical laws, or (number of) spatial dimensions. Isaac Asimov's novel The Gods Themselves is a classic example, with its utterly different intelligent aliens. Greg Egan's novel Diaspora features mind-bending descriptions of a four-dimensional universe.
Planetary Romance is an operlapping subgenre that shades into the vast 'romance' genre. In this case, the love story is embedded in futuristic (or fantastical) technology, and the striving lovers can be separated by more than Earthly distances. Edgar Rice Burroughs' "Barsoom" series features luscious Martian princesses, while Andrew M. Greeley's novel Final Planet does a good job of fusing these often disparate literary styles.
Post-apocalyptic stories are set well after some vast upheaval. Rather than showing the immediate aftermath, these tales depict a new society that has arisen from the ashes, usually here on Earth. Often the survivors remain leery of technology, as in Edgar Pangborn's classic novel Davy. (Its Holy Murcan Church maintains a ban on gunpowder, along with "anything else that might reasonably be construed to contain atoms.")
Posthumanism is a subgenre tied to a philosophical type movement. (Going beyond the percieved limits of traditional Humanism, as expressed in fiction.) In practice it's very close to Transhumanism, and is controversial even to define. Charles Stross's novel Accelerando is one example.
Robot SF tales are self-explanatory. In a sense, the concept of robots predates SF itself, and the two visions have developed in parallel. Isaac Asimov's many "Robot" stories are a preeminent example. One of the earliest such novels is Adam Link, by Eando Binder.
Science Fantasy is an overlapping subgenre, comprised of stories that meld the SF and Fantasy genres, and tilt toward SF because they feature advanced technology such as spacecraft. Many of the works of Andre Norton, and Anne McCaffrey's "Pern" franchise, fit this subgenre.
Soft SF focuses on the future development of the 'soft' sciences, rather than gadgetry. Ursula LeGuin's "Hainish" novels are good examples. Isaac Asimov's "Foundation" novels feature a predictive social science called Psychohistory.
This is a vast subgenre, whether or not its protagonist travels in space as well. In these stories, this capability is possible, and is put to use by the characters -- in secret or in public, and rarely or often. The effects of such temporal ventures vary in each portrayal. (With paradoxes, new timelines, historical immutability, etc.)