Readers like genres because they are familiar. Readers choose a genre because they've enjoyed other, similar books. They know more or less what to expect, and that helps them imagine the fictional world and the people who populate it. Going to a familiar genre can be like going home. Readers probably have friends who enjoy the same genres, so there can even be a sense of community. Fan fiction is a testament to this community.
Authors like genres because they provide a platform for world building and character types. Many genres have tropes that authors can exploit in constructing plots, creating quirky characters, and inserting tension. Even literary fiction can mine the resources of genre. Many calls for short stories specify genre. Whether you intend to write genre fiction or not, it's worthwhile to know and understand at least some of the basics of a few genres.
Some genres target reader demographics rather than deploy specific fictional forms. For example, young adult and near adult are both recognized market segments that can use any of the genres listed in this stroll.
This is a survey of some of the major genres and their sub-genres. It's eclectic rather than inclusive. People can't even agree on what the genres are let alone the definitions, although the sub-genres are generally clearer. Moreover, many novels cross genres. The TIme Traveler's Wife is both a romance and science fiction, for example. Is A Connecticut Yankee in King Arthur's Court a historical thriller or science fiction, or something else? Ultimately, it's your call as author and reader.
This is just one guy's opinions on genres. It's a start, but don't take it as gospel.
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Science fiction usually refers to stories which explore how imagined scientific or technical discoveries change society and the everyday lives of people. There are many subgenres and cross-genre possibilities.
Speculative fiction tropes. 
Dystopian/Utopian. Novels like Orwell’s Nineteen-Eighty-Four or The Dispossessed by Ursula LeGuin are examples of this sub-genre.
Space Opera. Star Wars, Star Trek, or Dune are all examples.
Alternate History. Star Trek is set in an alternate history. Dick’s The Man in the High Castle is an alternate history where the Nazis won WWII.
Cyberpunk. A form of dystopian alternate history. Johnny Mnemonic and Necromancer are examples.
Steampunk. A form of retro-futuristic alternate history based on nineteenth century technology. H.G. Wells’ The Time Machine or The Difference Engine by William Gibson and Bruce Sterling are examples.
Military SF. These stories consider consequences of scientific or technical discoveries in a military context. Keith Laumer’s bolo series is an example, along with Jerry Pournelle’s Falkenburg books.
Romantic SF. Romance is the focus here. The movie Her is one example. The Time Traveler’s Wife is another.
Hard SF. These stories pay particular attention to scientific accuracy and logic. Examples are The Andromeda Strain or The Martian.
Soft SF. These stories may include scientific or technical advances without explaining the scientific basis or—sometimes—deal with so-called soft sciences like sociology or history. Examples might include light sabers in Star Wars, most faster-than-light drives, or Daniel Keyes’ Flowers for Algernon.
Time Travel. Stories involving travelling to different times, either in the future, the past, or both. These cross several other genres and subgenres, and are generally soft SF. Poul Anderson’s Time Patrol is an example.
Slipstream. When applied to SF, this might include interdimensional travel, or travel to another universe with different physical laws, or just a generally weird event. Vonnegut’s Slaughterhouse Five is an example. Kafka’s Metamorphosis is another.
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Every romance story has two basic elements: a central love story and an emotionally satisfying and uplifting ending. Again, this basic form admits many crossover and subgenre possibilities.
Romance novel tropes
Paranormal Romance. A romance that includes paranormal things, like ghosts or telepathy. Ghost is an example from cinema.
SciFi Romance. Any SciFi story can include the essential features of a romance. The Time Traveler’s Wife is certainly an example.
Contemporary Romance. Set in the modern world. The Notebook is an example.
Western Romance. Set in the US West, usually but not always in the late nineteenth century. Legends of the Fall and Brokeback Mountain would be two examples.
Gothic Romance. These stories have a dark atmosphere, filled with mystery, suspense, and—sometimes—supernatural elements. Wuthering Heights and Edward Scissorhands are examples.
Romantic Suspense. Rebecca by Daphne Du Maurier or Fifty Shades of Gray are examples.
Regency Romance. These are romances set in the early nineteenth century, usually set in the British Isles, and usually inspired by Jane Eyre. The Regency is a period of British History from 1795-1837, although the official regency of George III only spanned the years 1811-1820.
Historical Romance. Any romance set in an historical era. E.M. Forster’s Maurce qualifies, as does Pride and Prejudice.
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There's a crime to solve. There's a detective to solve it. Infinite variations.
Mystery tropes
Noir/Hard Boiled. This darker form of mystery typically features an anti-hero detective battling a dark underworld and corrupt system. Works like Hammett's The Maltese Falcon and novels like those of Raymond Chandler typify the genre.
Cozy Mystery. Typically these include an amateur sleuth, set in small, intimate communities, and where sex and violence occur off-stage. Agatha Christie's Miss Marple series, or Lillian Jackson Brown's Cat Who...series are examples.
Historical Mystery. Set in a past historical era. Umberto Eco's The Name of the Rose is an example.
SciFi Mystery. A mystery in a SciFi setting. Isaac Asimov wrote a series of stories with a robotic detective. Larry Niven's Gil the ARM is a future detective who investigates harmful new technologies.
Police Procedural. These mysteries focus on police and forensic techniques. The CSI TV series is an example. Joseph Wambaugh wrote many in this genre, such as The Choirboys.
Hobby Mystery. This is a subset of the Cozy Mystery where the sleuth has a niche hobby or engages in a craft that is connected with the crime. The BBC series Lovecraft involved crimes where the protagonist's expertise in antique restoration (and forgery) played a part. Sarah Atwell has a series of mysteries involving glass blowing.
Paranormal Mystery. The crime involves paranormal elements, or the paranormal helps to solve the crime. Stephen King's Later is an example.
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A character in jeopardy dominates the plot. Pursuit, escape, and cliffhangers plague the characters. Suspense also characterizes these novels. There's usually a dark and hostile person or group who threatens the protagonist. This genre readily crosses with myseries, romance, and science fiction.
Thriller tropes
Environmental Thriller These involve an environmental calamaty which may or may not be global in scope. One of the first examples was No Blade of Grass, an 1970 SciFi movie. Tourist Season by Carl Hiasson is another example.
Supernatural Thriller Thrillers with a supernatural element. Dean Koontz often writes in this genre--for example, Dragon Tears. Stephen King's Carrie is another.
Historical Thriller A thriller set in an historical era. King's 11/22/63 is one example. Ken Follet's The Pillars of the Earth is another.
Medical Thriller Usually these are set in a hospital, involve medicine, and a protagonist who is a physician or knowlegeable about medicine. Robin Cook has made a career out of writing these. Michael Crichton's Andromeda Strain is another exmample.
Psychological Thriller Here, the focus is on the mind--that of the criminal as well as the protagonist. Silence of the Lambs is an example. The Sixth Sense is an example from cinema.
Legal Thriller These focus on crimes, the law, lawyers, courtrooms, and the legal system in general. Many of John Grisham's novels fall in this category. The 1985 Harrison Ford vehicle, Witness, is an example from cinema.
Spy Thriller These feature spies, secrets, double-crosses, and complex plots. The Bourne Identity, The Day of the Jackel, The Spy Who Came in from the Cold, and anything by Ian Fleming are examples.
Politcal Thriller Politics and politicians are the name of the game. The stakes are high, the opposition powerful, pervasive, and corrupt. Seven Days in May is an example, as is The Pelican Brief.
Techo Thriller Technology is the star--or the villain!--here, and the details are important, so get them right. Often these have SciFi elements as well. Dan Brown's Digital Fortress, or Neal Stephenson's Crytonomicon are examles.
Military Thriller It's all about war and the people who fight them. Anything by Tom Clancy fits, but many authors write in this popular genre.
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Fantasy involves fantastic elements that can't exist in real life. These can include magic, spirits, mythological creatures, beings from other dimensions or realms. Sometimes the story is set in an alternate fictional world, but sometimes the fantastic elements apppear in conventional settings.
FantasyTropes
Traditional Fantasy These have the feel of folk tales, tall tales, fairy tales, fables, myths, and legends. They often include fairies, elves, trolls, and other creatures of myth and lore. Lord of the Rings is an example of this kind of fantasy.
Urban Fantasy The supernatural arises in a contemporary urban setting. The supernatural can be mythic creatures or just wierd and spooky. The protagonist often has a foot in both worlds, and the contemporary world often borrows from the noir tradition. Jim Butcher's The Dresden Files is an example. The 1970s TV series Kolchak was a comic version of the sub-genre.
Contemporary Fantasy Urban fantasy without the urban setting. The Twilight series is an example.
Historical Fantasy Fantasy in the past. The Book Theif, by Markus Zusak, is an example. Bergman's The Seventh Seal is an example from cinema.
Horror Here, the purpose is to create feelings of dread, repulstion, and fear in the reader. Horror can be a sub-genre of thriller, too, but it often involves supernatural elements, as in The Shining.
Super Heros Whether it's Spiderman, Superman, or Wonder Woman, super powers are fantasy. Hollywood cranks out endless examples. New and fresh appears to be not required for the Hollywood versions, but these can provide multiple opportunities for originality and creativity. Super-heros might also fit in the SciFi category, depending on whether the author makes a nod to science in explaining the super-powers (Superman and Spiderman, for example) or uses mythology or some other similar basis as an explanation (Wonder Woman).
Slipstream We included this in SciFi, too, for cross-dimensional travel. In fantasy, it might involve visiting magical realms, distinct from our contemporary, humdrum world. Wierd is another characteristic of slipstream. Borges' The Aleph and Other Stories is a literary example.
High/Epic Fantasy The setting isn't Earth as we know it, and certainly isn't now. Whatever it is, there are supernatural forces that threaten its existience, or at least the existence of the protagonists. Supernatural forces may also be the saviing grace of the protagonists. Andre Norton's Star Gate is an example. Better known would be Game of Thrones.
Paranormal Paranormal stories involve elements outside of conventional reality that have concrete, observable consequences in the fictional world. Most stories with vampires or werewolves fit this definition, as do most stories with extra-sensory perception. Many ghost stories do as well. There may be an initial mystery about what's going on, but eventually all is explained through a reveal of who--or what--is causing the paranomral element.
Supernatual Supernatural stories are similar to paranormal, except that the source of the paranormal/supernatural element is unknown and, ususally, unknowable. Many ghost stories fall in this category--was that really a ghost or just an hallucination? Stories about the afterlife, the soul, or gods are other rexamples. The source of the supernatural remains a mystery. These stories take to heart the words of physicist Arthur Eddington: The world is not only stranger than we imagine, it's stranger than we can imagine.
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