Crossovers are familiar to every writer, and more often than not the result of a daytime fancy. They're quite fun. There are two types of crossovers. The first and most common type is that you take characters from one universe and toss them in with another set of characters from a different universe or time. The second and less noticeable type is taking characters from one universe and making them play by the rules from a different universe. Introducing telepathy into wizardry would be a good example of this, or having a witch spring up in Professor X's school would be another.
This time we'll deal with the first type. The possibilities for disaster in a crossover are many, so I'll just provide three commands and seven suggestions I've learned from reading and writing crossovers, both good and bad.
Do's
COMMANDMENT #1 (Note: NOT suggestion, but command): Thou shalt explain. This is the number one rule in fiction, and it applies here as well as anywhere. Everything must have a why. Everything. If Harry Potter suddenly winds up in Tortall, there had better be a reason why. Interference of the gods, accident in Potions, whatever; make a reason. The characters, though, don't necessarily have to know the reason, just make sure the reader knows by the end.
COMMANDMENT #2: Get it right. This rule, a staple of fanfic, goes double for crossovers because there's twice the potential for mistakes. Your facts must be accurate else your credibility in the eyes of your reader is gone. If you do change the rules, see #1.
COMMANDMENT #3: Have fun in the writing. If you're not having fun, the reader won't. So feel free to break all suggestions and just let the characters run wild. Do something unplanned, or just run with an idea. Writing is supposed to be fun, it must be fun to flourish.
Now, on with the suggestions. Keep in mind these are suggestions, and can be broken or disregarded.
Suggestion #1: Give the characters a common enemy. As Harry found out in The Philosopher/Sorcerer's Stone, nothing can seal a friendship like beating the bad guy. A common enemy can also serve Commandment #1 - one set has to go get the other set, and the two must work together to win. The converse of this is also fun; pit the characters against each other.
You don't need an enemy, you could just plop the characters together in a time of peace and let them have fun, as a vacation of sorts.
Suggestion #2: Let sparks fly. If one character really likes the other, go ahead and let them fall in love. Even let one of them stay in the other universe if you want, though I'm a sucker for characters that put duty to their universe above love, and I'm not the only one. ;)
Suggestion #3: There's no such thing as a big, happy family. The characters you throw together don't have to like each other. Antagonism and squabbling make for fun comedy, and can add an edge of realism to your fiction.
Suggestion #4: Have the characters learn something, or make an issue of the fact they don't. One of the best Star Trek/Star Wars fanfic I read was by the late Lady Aerin. R2D2 and 3PO, after meeting Data and watching the Enterprise crew react with him, realized that they were sentient and wanted to be acknowledged as such. Han refused to see Data, R2 and 3PO as anything other than droids, while Luke realized that alive meant more than being sensed in the Force. That caused a lot of friction between them. The Star Wars crew went home, but didn't forget what they'd learned, and R2 & 3PO pushed for sentience. In the end, the Senate, to "stop a possible droid rebellion," forced Luke to delete his droids' memories of the Enterprise and the lessons they'd learned there, or else destroy the driods. In a different ST/SW fic by the same author, Captain Picard became the first Federation Jedi.
Suggestion #5: KISS - keep it simple, Sam. The biggest mistake one can make is putting too much together at once. You know how much you can handle, but generally three universes is the limit. After that things can get messy (the 7th D B&G is an exception. Chaos is expected there). Some of the worst crossover fanfics happen where the author throws 20 characters from 10 different universes together. If you can do it well, go for it - my email's dragonladykhushrenada@yahoo.com. But know your limits.
Suggestion #6: Stay in character. Just because the character is in a new place doesn't mean he stops being who he is (once again 7th D is the exception). You must stay in character or provide a reason for the change. If you don't, you face a loss of credibility.
Suggestion #7: We're a universe, too. Sending fictional characters to our world can be a lot of fun and a jolly good read. Keep in mind some characters may not take the revelation their life is fiction well. *cough* *cough* Snape! *cough* *cough*