A crossover is a fanfic in which two or more fandoms are combined in some way. Crossovers are an old story trope of fanfiction; as soon as fans started writing stories in more fandoms than just Star Trek, they started crossing those sources together. In story notes, a crossover is frequently notated with an 'x', so a Star Trek story crossed over with Star Wars is sometimes written as ST/SW and sometimes written ST x SW.
Crossovers may take place in many ways. In the most common form, characters from Fandom A may meet characters from Fandom B (i.e., a Stargate Atlantis story in which The Doctor visits Atlantis, perhaps with a Companion or two in tow). Crossovers can involve as many fandoms as the author(s) can juggle; there's no limit to the potential madness and creativity of the exercise.
A form that is most common in Harry Potter crossovers, but sometimes seen in other fandoms with canon orphans (or characters who can easily be made to be orphans), is the adoption fic, in which someone from another fandom (generally selected for their kick-ass qualities) brings up the orphan.
Many fandoms use canon incidents or devices to facilitate crossovers. Star Trek's canon holodeck can be used to introduce characters from any other fandom, and its time travel allows crossovers with present-day or historical settings. In Buffy fandom the first Halloween episode involved enchanted costumes which made the wearer take on the personality of the person depicted; in the episode these were generic characters - soldiers, ghosts, etc. - and the effects wore off at the end of the spell, but in fanfic the costumes are often used to give Buffyverse characters the personality and sometimes powers of e.g. a superhero, often permanently. This trope has been borrowed by many other fandoms. Doctor Who introduced the "chameleon arch" which turns Time Lords into normal humans with false memories, revealed only when they open a device that contains their memories; this is often used in fanfic to turn characters from other fandoms into Time Lords.
Some crossovers are almost subliminal, like cinematic Easter eggs, briefly using e.g. a character or device from one canon in a story set in another, which may go almost unnoticed. They are occasionally seen in canon as well as fan works. For example, The Laughing Fish, an episode of Batman: The Animated Series, has a scene in which Joker tries to kill Batman with a wrench he grabs from a box that appears to have a partially-obscured Binford Tool label, a Home Improvement reference. Buzz Lightyear is imprisoned in a box with the Binford logo in Toy Story. Similar minor crossovers are common in fan works.
Fusions are a kind of crossover or AU where characters from one fandom (Fandom A) may be imported into the setting of another fandom (Fandom B). Fandom A characters may take on the roles of Fandom B characters (i.e., a Stargate Atlantis story in which John Sheppard is a Sith lord and Rodney McKay is a Jedi) (perhaps in a story strangely like this one: The Dark Side, by Astolat) and not interact with Fandom B characters at all, or only very peripherally.
Crossover fusions with romance movies (An Affair to Remember, American Dreamer, You've Got Mail, etc.) have been written in slash forever, but for some reason, they're rarely considered crossovers; they're just considered AUs, perhaps because the romance movies rarely have a fandom following of their own.
A special case are crossovers between sources that share the same actor, e.g. between SGA and Traders which both star David Hewlett. These same-actor crossovers sometimes draw criticism for requiring more suspension of disbelief, and in the case of same actor pairings also for blurring the line between character and actor slash, especially in the past when RPS was less widely accepted. In some cases these crossovers even rate their own pairing names, communities and challenges. For instance, in SGA fandom, a common crossover technique is to write a character of David Hewlett's (from a show other than SGA) in a romance with a character of Joe Flanigan's (also from a show other than SGA) - this crossover pairing is known as Hewligan, and can refer to a variety of pairings (i.e., Grant Jansky (Traders)/Pete Sherman (Sherman's March), or Michael (Century Hotel)/Nick (Farewell to Harry).
In other cases, two characters played by the same actor turn out to be the same person; for example Claude Rains from Heroes turns out to be the Ninth Doctor in disguise, or Ducky Mallard from NCIS is actually an older Illya Kuryakin from Man from Uncle. See also the Six Degrees of Jeremy Renner trope, in which all characters played by Jeremy Renner (Hawkeye in The Avengers) are Clint Barton in disguise, siblings, clones, etc. A canon non-crossover example is the case of the vengeance demon Halfrek in Buffy the Vampire Slayer, played by Kali Rocha who had previously played William's (pre-vampiric Spike's) love-interest Cecily. In a later episode it was revealed that Halfrek was Cecily; comics canon says she was already a demon when William was in love with her.
Stories in which characters played by the same actor are mistaken for each other, or impersonate each other, are also common. For example, Nathan Fillion played the murderous preacher Caleb in Buffy, and author Richard Castle in Castle; a standard trope seen in most crossovers between the shows has Buffy characters attack Castle as soon as they see him, assuming that Caleb has somehow come back to life. In non-crossover canon much of the plot of Orphan Black revolves around repeated cases of same-actress impersonation or mistaken identity.
These themes can be inverted in stories in which different versions of the same character (portrayed by different actors or in different media) meet; for example, versions of Superman from Superman Returns and Lois and Clark: The New Adventures of Superman, Sherlock Holmes from Sherlock and Elementary, etc. Usually the explanation involves Alternate Universes. There is also the canon non-crossover case of the Buffy episode The Replacement, in which two different actors, Nicholas Brenden and his twin brother Kelly Donovan, play Xander Harris so that two versions of him can meet.
Another variant of actor crossover is a crossover between the fictional and "real" worlds, with actors meeting or swapped with the characters they play; for example, Jensen Ackles meeting Dean Winchester, Robert Downey Jr. swapped with Tony Stark, etc.
Same name crossovers
A common if somewhat unimaginative trope takes two fandoms which happen to have characters with the same name. "Obviously" they're related! An example is Scott Summers and Buffy Summers, and there are several stories where they are cousins or otherwise related. This can be stretched slightly by ignoring differences in the spelling of the surname - e.g. Jamie Somers (The Bionic Woman) is also related to Buffy, but a different branch of the family that changed the name slightly. There are stories where Samantha Carter (Stargate series) is related to Agent Carter (Marvel) or Sheriff Carter (Eureka). It's even occasionally extended to fandoms where characters have common first names, if the name is rare enough; e.g. Xander Cage (the XXX series) and Xander Harris (Buffy).
An alternative approach is to treat common names as a coincidence which results in the events of the crossover; e.g., Buffy and Scott happen to reserve rooms at the same hotel and the desk clerk somehow thinks they're married and ends up putting them into the same room; or a message intended for the Watcher Bernard Crowley (Buffy) ends up going to the fallen angel Crowley (Good Omens). This approach is comparatively rare.
Using official crossovers
In some fandoms, it's not unusual for two or more fannish sources to have crossover episodes or events in canon. Typical examples are comic company crossovers between DC and Marvel, like the JLA vs. Avengers mini-series, and crossovers between Batman and Judge Dredd, Predator, etc. TV shows (especially ones made by the same production company) also do crossovers, such as those between Eureka and Warehouse 13. The latter can be double episodes like between CSI: Las Vegas and Without A Trace (or back in the day, between Magnum PI and Simon & Simon) or implied crossovers through character appearances, like of Homicide's John Munch showing up, in character, on the X-Files. An unusual example was the X-Files episode X-Cops which was a crossover with the "reality" crime show Cops, though in this case using actors instead of real police. In some TV series the official crossover implications are almost byzantine through a series of such overlaps, and tracked on fansites devoted to this phenomenon. Doctor Who and Torchwood are so intertwined that many authors and sites consider them to be a single fandom; The Sarah Jane Adventures also derive from the same canon, and stories that mingle canon from all three shows plus spinoff novels etc. are moderately common.
Crossovers and meta
Sometimes the point of a crossover is a contrast and compare of the fannish sources. A meeting in a bar between Duncan (of Highlander) and Buffy, talking about the pain of being a Champion, or between Methos and Krycek, talking about the fun of being morally ambiguous killing machines. Sometimes the point is even broader, such as commenting on the pain of being a black sidekick, as in Them Mean Ol', Low-Down, Lando Calrissian Blues, by Yahtzee, or the trials of being a fictional character popular in slash fiction, as in Support Group for Fan Fiction Characters: First Meeting, Slash Chapter by Cousin Shelley.
Ofttimes crossovers are an answer to the problem of a much-loved character who lacks a shippable partner in his or her source fandom, or else an answer for a writer who only likes one character of a popular pairing -- like Methos, but not Duncan? Write Methos into another universe altogether! Certain characters seem to lend themselves to showing up in other universes; they are sometimes referred to as Little Black Dresses of fandom.
: Writing a crossover has its own dangers, the difficulty lying somewhere between single-media and professional writing. I like to write them because they add a bit of spice to a story and provide a challenge. I rarely enjoy reading them, however, because they're often poorly done; the writer or editor can't handle one of the shows involved or doesn't know enough about it, one of the shows is sacrificed for the glorification of another, humorous crosses aren't half as funny to the reader as they seem to the writer and editor, etc. Barring copyright problems, even television has problems with crossovers (does anyone remember the Magnum, P.I. and Murder, She Wrote crossover, where Magnum looked like a raving idiot and Jessica Fletcher came off as a meddlesome old hag?). Crossover fiction can be written and written well, no matter how outrageous the crossover. 
Examples of crossover fanfiction
- A pre-internet crossover is A Meeting in the Hyades by Marion Zimmer Bradley, in which Aragorn from The Lord of the Rings appears in an early version of Darkover; first published in 1961 but written in the 1950s.
- An example from 1954 - Dorothy L. Sayers wrote The Young Lord Peter Consults Sherlock Holmes for the BBC's Radio Times magazine.
- One of the earliest online multifandom crossovers was "The Witness" by Michele Martin, which crossed X-Files, Forever Knight, Highlander, Starman (tv), and Quantum Leap, along with several cameos from other fandoms. It was archived on Gossamer on May 16, 1995.
- Wherever You Stand A Hundred Shall Fall by James Walkswithwind is a Batman/Sentinel crossover ~ 1996-7
- When Hellmouths Collide by Kimberley Rector and Martha Wilson is a Buffy the Vampire Slayer/Hercules: the Legendary Journeys crossover. (1999-2002)
- Them Mean Ol', Low-Down, Lando Calrissian Blues is an influential humorous multifandom crossover by Yahtzee, highlighting the underutilisation of male characters of color in popular television shows (January 2002)
- Hell Money by FayJay is an early example of Buffyverse/Smallville, which would prove a rich crossover playground (May 2002)
- The End of the Beginning by Mariner is a popular early Buffyverse/Harry Potter crossover (2003)
- Laura Mason's "Wrightsville: Long Ago and Far Away" is a crossover between The Charioteer and Ellery Queen (2006–7)
- Dust in the Wind by Lyrawing was a SPNxAmerican Gods story (March 2007)
- And All the World Beneath by Seperis was a famous SGAxSPN story (August 2007)
- Supersaturation by SkoosiePants is SGA/Bandom (2007–9)
- "House of Cards" by nevoreiel and "Escape from Solitude" by mysid are crossovers between Torchwood and Mary Renault's novel, The Charioteer (2007 & 2010)
- Angel, Dr. Horrible's Sing-Along Blog: In Memory of Penny Lesse by Jedi Buttercup. Just when you feel you've almost drowned, you find yourself on solid ground. (2008)
- "You Are Cordially Invited" (and its sequels) by fawatson is a futurefic crossover with characters from at least four modern novels by Mary Renault (April 2008)
- The Kingdom of the Blaggers by Hackthis is a crackfic fusion: "The problem with being the son of Uther Pendragon, legend of stage and screen, winner of Emmys (twice), Tonys (once), Oliviers (multiple), BAFTAs (twice), Oscars (once) and People's Sexiest Man (twice) was that nobody was ever going to take Arthur seriously as an actor in his own right." (2009)
- Labyrinth, Pan’s Labyrinth: A Lost Child in a Forgotten Tale by amelia_petkova. Ofelia wishes her brother away but not for the reasons you might think. (2010)
- "Confidence Lost" is a 33-chapter Batman/White Collar crossover by C.R. Scott (2011)
- Buffy, Teen Wolf: Botched by Rivulet027. Derek botched Dawn’s rescue attempt or Dawn botched Derek’s rescue attempt. Either way Stiles and Isaac rescued themselves. (2012)
- The Avengers Movieverse, Doctor Who: Make It Your Strength series by kerrykhat. "I'm Doctor Martha Jones," she told the pale man in the black, gold, and green armor who had invaded UNIT. "Who the hell are you?" (2012 – now)
- The Avengers Movieverse, Hansel and Gretel: Witch Hunters: By Any Other Name by [Liannabob]. "A Clint/Hansel mindswap fic with a whole lot more plot than that statement might imply. I mean, lots of crossover shenanigans, of course. But also a plot." (2013)
- Superman Returns, Lois and Clark: The New Adventures of Superman: The Planes by Dandello. "When Superman and Lois are thrown into a world where Clark Kent is EnC of the Daily Planet and married for ten years to Lois Lane, things get more than a little strange for both sets of Lois and Clark." (2006-7)
- Harry Potter, Stargate SG-1, Buffy, Batman, The Bionic Woman, The Secret World of Alex Mack: The League of Extraordinary Women by Diane Castle. "Hermione Granger has to recruit six women to help her stop an army of monsters before her world is overrun. But none of the women are even in her dimension…" Start of a series now running to nearly two million words, taking in dozens of fandoms, with "side stories" by at least nine other authors.
- Sherlock, Elementary: Elementary, My Dear Sherlock by Eltuine. "Joan Watson wakes up in an unfamiliar house in an unfamiliar city, with an unfamiliar man staring at her, claiming to be Sherlock Holmes. Meanwhile, on the other side of the ocean, John Watson finds himself in a similar situation. When each Watson tries to return home, however, difficulties arise. How will both Sherlocks deal with the removal of their respective Watsons, and how will each Watson get back to where they belong?" (2013- WIP)
- Star Trek: The Next Generation, Buffy: Legend by Shayne Terry. "Trapped by an alien collector, Lieutenant Commander Data discovers an early 21st century android excavated from the ruins of Sunnydale and a capsule containing the frozen body of one of the Eugenic wars most notorious figures...Buffy Summers." (2011)
- Young Wizards, Callahan's Bar series - Spider Robinson: Callahans by Avida calandia. Considering the precedent set by our predecessor, Callahan’s Place, we should’ve known it would only be a matter of time before something strange and wonderful walked in. (2012)
- Buffy, X-Men: Buffy and the X-Men by Plato: Buffy runs away to New York instead of LA in hopes of starting a new life. (2003)
- Mr. Benn, The Invisibles, RPF: Mr. Benn: Invisible by dontmakeeyecontact. When Jack Frost and Jolly Roger find they need to break into a record company’s impregnable headquarters they call upon the help of a singular individual. Crossing a popular British children's cartoon series of the 1970s with Vertigo's The Invisibles and rock RPF. (Date unknown)
- Doctor Who, Nero Wolfe: The Orchid Thief by leviathan: Nero Wolfe and Archie Goodwin have solved a lot of tough cases in their careers as detectives. But never one like the one that begins with the new arrival in the Plant Rooms. Before it ends, they'll deal with a tattooed lady, miniaturized corpses, and Things from Another World! (2009)
- Addams Family, Angel: Her Beauty and Her Terror by ijemanja: Amanda Buckman moved to California, changed her name, and became a vampire. Wednesday can't help but approve. (2007)
- Buffy, Avengers, Supergirl: Origin Story by Worldmaker: Halloween ends, and Xander finds himself in a place he never thought was real, under circumstances he never saw coming. (2013-2016 WIP)
Thematic Lists for crossover fic
- list of Starsky and Hutch crossovers
- Recs tagged crossovers/fusions at Fancake
- List of Forever Knight crossovers by fandom
- Same Actor Crossovers (response to Lucy Gillam), Shomeret at The Fanfic Symposium (1999)
- Any *NSYNC/XF crossovers????; archive link (April 2000)
- The Ten Commandments of Crossovers, Lucy Gillam at The Fanfic Symposium (2001)
- Crossovers, Kadorienne at The Fanfic Symposium (2002)
- Crossovers - shared_wisdom, Archived version Jane Davitt, (2008)
There is a fannish newsletter for crossovers, crossover_news, and an archive, Crossoverfic.com. The Buffy fandom has its own archive for crossover fanfiction, Twisting the Hellmouth. There is a similar Stargate archive, Wormhole Crossing, but it has been off line since early 2015.
- Lucy Gillam. Joxer?! And Other Things I Don't Get. Posted 24 November 1999. Accessed 3 October 2008.
- For example Dean Winchester (Supernatural)/Chloe Sullivan (Smallville): Winsullivan and Winchullivan, with Chlean being a common pairing name.
- The Hewligan Fiction Archive; The Hewligan Fest community.
- Poobala.com's Crossover Spin-Offs Master Page
- Them Mean Ol', Low-Down, Lando Calrissian Blues - Yahtzee
- "Support Group for Fan Fiction Characters: First Meeting, Slash Chapter" by Cousin Shelley
- from Psst... Hey Kid, Wanna Buy a Fanzine? #1