A crossover is a fanfiction that combines two or more fandoms. They range from the almost likely to the completely implausible. Crossovers of the implausible variety are dealt with by the Department of Implausible Crossovers (DIC), which is headed by the Lichen. Real World crossovers are the purview of Despatch.
A crossover may be called a megacrossover if it involves an unusually large number of continua. Tropedia defines a megacrossover as "a fan-made creation combining three or more properties into a single, hopefully coherent, whole." Key word: hopefully. The more continua involved, the more implausible it tends to become.
Types of Crossovers
The most common kind, a standard crossover occurs when a fanfic author smashes together two continua that are not canonically connected. This can be done very successfully, or it can leave the reader going "WTF?" It is very common for people to decide that Harry Potter and Yu-Gi-Oh!, for example, have the same planet Earth as a setting. Or to write about Star Wars and Star Trek taking place in the same universe.
Goodfic that does this meshes the worlds sensibly and interestingly. Badfic that does this leaves gaping plotholes trying to explain away where incompatible plots in two different works of fiction would otherwise make each other impossible—or even worse, doesn't even try to make sense of it at all.
The Harry Potter continuum has very many standard crossovers. It is a generally acknowledged rule that if a fandom exists, it has been crossed with Harry Potter.
Real World Crossovers
Continua can be uncanonically connected to the Real World by virtue of a character from one world traveling to another by means of trans-dimensional hopping or snatching. Technically these stories are a type of crossover, but the contact between the two worlds is usually limited.
Very often, the main character from the Real World half of the crossover is a self-insert or an avatar. These character types are very prone to becoming Mary Sues if they fail to act, think, and grow as a real person would.
In the case of trans-dimensional hopping, the crossover is done by an OC traveling from the Real World to a canon world of his or her choice. When this is done well, you get something like "Don't Panic!" by Boz4PM, which explores the logical outcome of a modern woman dropping into an ancient world where she doesn't even speak the language. When this is not done well... see Mary Sue.
In the case of trans-dimensional snatching, an authorial influence or Mary Sue transports canon characters from their home continuum to the Real World. "BagEnders" is an example of this type of story done well. Unfortunately, what often happens is an insipidly cute sleepover at the writer's house, or all the members of the Fellowship becoming stereotypical teenagers at the same high school.
An actor crossover typically involves a character meeting another character played by the same actor. This type often results from the same actor playing parts on two popular television shows or movies. (For example, David Tennant in Doctor Who and Harry Potter and the Goblet of Fire, or Derek Jacobi in The Golden Compass and I, Claudius.) There are usually many bad jokes about how the two characters look like each other.
It is likely that Benedict Cumberbatch will be subjected to this treatment, due his present or future roles in four major franchises: Sherlock, The Hobbit, the Marvel Cinematic Universe, and Star Trek Into Darkness.
Another type of actor crossover is a variety of Real Person Fic in which an actor enters a canon continuum and meets the character he plays. This type is less common, but also involves bad jokes.
According to Architeuthis, in this type of crossover, "different canonical characters from different continuums [sic] are 'revealed' to be actually the same person." For instance, "Well, Gandalf and Dumbledore are both magic-users with long beards, so... wow, they must be the same person!"
When the same principle is applied to canon settings, you get a standard crossover.
These are crossovers that takes place in the actual canon. They're practically a standard feature in comics and they can also occur when two or more television shows are owned by the same network or when a show has several spin-offs. The Disney Channel is rife with canon crossovers. Star Trek has quite a few as well, since there are five series, some of which are supposedly set during the same time period. It even has a crossover movie.
They're somewhat less common in books, but not unheard of. For example, Percy Jackson and related canons all take place in the same 'verse; in fact, Magnus Chase, titular character of the Norse series, is the cousin of Annabeth, one of the main characters of the core series. For another example, the Young Wizards series contains a stealth crossover with Doctor Who: a man with a suspiciously familiar scarf appears in a scene at an interstellar crossroads.
Crossovers and the PPC
The "Tangled Web" fiasco in 2002 saw almost the entire DIC called in to handle an out-of-control megacrossover involving at least five continua; more if you count all the Star Trek series separately.
The 2013 Blackout can be seen, in a way, as a giant PPC/Almost Every Other Continuum crossover, with various canon characters and monsters finding their way into HQ through the destabilised shielding. Some of these canon characters include: the Eleventh Doctor, Clara Oswald, Dean and Sam Winchester, Castiel, Crowley, Aziraphale, Albus Dumbledore, Hermione Granger, Sherlock Holmes, John Watson, Rumbleroar (and just about any other continuum's cats), Batman, Superman, and Robin. Some canon monsters include: Creepers, Weeping Angels, and Timberwolves.
PPC agents were also thrown into other continua during the Blackout. Those continua include Aperture Science and Knightmare.
- Lily's Tutorial on Fandom Collision (NSFW)
- An illustrated guide by Lily Winterwood on how to distinguish the most common types of crossovers and how to avoid the pitfalls of writing them badly (hint: know your fandoms). It's easy to read, easy to print and easy to bring on missions, if you are new to crossovers.