There are two, closely related types of fanfiction that have some unique challenges: Alternative Universes and Cross-overs. Alternative Universes are where the writer deliberately changes the setting the characters are in, from changing one event early in the story, to completely moving them to a different time/place. Cross-overs are where you take two or more fandoms and merge them together somehow.
Two of the more common AUs are the vampire trope, and the high school trope. In the vampire trope, one or more of the canon characters are turned into vampires. This obviously changes things, as characters suddenly become immortal, nearly indestructible, etc. Of course, the bad guys may be vampires, too, so the dynamics can be basically the same, just with new powers. This AU trope seems to vary in popularity, with spikes happening when Interview with a Vampire, Laura K. Hamilton’s series, and Twilight came out.
In the high school trope, adult characters are put into a high school setting, often as students but sometimes as teachers as well. Since many fanfiction writers are in school, themselves, this setting pulls the characters into a place with established dynamics that they know well. There’s something fun about having Bruce Banner as the temperamental science teacher, or Wolverine as the cranky football coach.
Another style of AU is to leave the setting alone, and ask yourself “What if this event hadn’t happened? What would have followed from that?” This can be things like Peter Parker’s Uncle Ben not dying, Jean Grey choosing Wolverine over Cyclops (and let’s be honest, Cyclops was a douche), or that first battle going different (worse or better). This can result in changes to characters’ personalities, or the way they relate to each other compared to the canon version. DC and Marvel comics have a long history of doing this type of “what if?” resulting in a “canon” that is so twisted, almost anything can be claimed as canon.
Another style of AU is to move the characters into a different time. For example, what happens if you move the Fantastic Four into 1692 (another what if that was actually done)? Suddenly, you have to reinterpret the characters in terms of the technology that existed at the time. They couldn’t be irradiated in space, but it could be something mystical. Moving characters from modern Japan to feudal Japan, or vice versa, is another possibility.
For all of these things, the challenge is to preserve the essence of the canon characters, while making them fit the new setting. For example, Wolverine will always be a reckless, loose canon, even if he does have the current love of his life with him. Then again, he’ll be haunted by all the other women he’s lost, and the fear of losing one more. Cyclops, on the other hand, would turn into more of a wannabe tyrant. Bruce Banner as a teacher might not turn into a green monster, but that doesn’t mean he couldn’t flip tables and cause gas explosions that destroy the school every other week. But keep in mind, he will always be a nerd.
The purpose of all this is to keep the fans of your fandom able to identify with the characters that they love. Things will change, but part of the fun is keeping the characters recognizable through all those changes.
A more interesting “AU” is the cross-over. In this, you look at multiple fandoms and find a way to somehow merge them into a single story. For example, who doesn’t want to see the Hulk smash that goody two-shoes Superman into the core of the planet? Normally, this would be impossible (Marvel vs DC), but in cross-overs, this is what we want. For some settings, it’s as simple as pretending they didn’t happen to meet before. For example, Aliens/Predator is a canon mixture. Wouldn’t it be neat to watch Wolverine become the leader of the Predators as they tear through an alien hive? How would Wolverine deal with a race with fake claws? How would the Predators react to a puny human with built-in claws? How bad would alien blood-acid hurt Wolverine? Is adamantium immune to that acid?
When you have the characters from different fandoms meet, you have to take special care to think about how they’ll react to each other. It is very easy to let one group of characters or another fall out of character. For example, what if Bruce Banner and Clark Kent became besties? What if Hulk and Supes became gay lovers? At last, Supes found someone who can withstand his “passion”, and Hulk can give someone a hug. We are NOT recommending this! Hulk is violent, not tender. Superman protects the innocent from all threats, which Hulk certainly is. This is a ridiculous example, but some people would try to do just this sort of nonsense, warping both characters beyond recognition.
When the settings are more different, new challenges arise. Crossing Star Wars with Teletubbies, for example, probably shouldn’t ever be done. But if you want to, you have to justify how they encounter each other. The intergalactic travel of Star Wars will be your key, here. Magic, super-science, and time travel can all be used to justify a variety of cross-overs. You can also mix a cross-over with an AU, moving several groups of modern characters into medieval Europe, for example. The Dark Knight Vader and his marauding army of knights could run into the Hulkish Ogre. The AU setting justifies bringing whoever you want in.
All the things being discussed here are just extensions of why we write fanfiction. The difference is that with cross-overs and AUs, we’re deliberately moving away from canon. Sometimes, it’s far, far away from canon. Despite that, you still have to remember the elements that makes a good fanfiction. Have good characters that the fans will recognize. Have good relationships. Have a good story.