One idea could be a crossover between Avatar: The Last Airbender and Harry Potter. Imagine Aang and his friends attending Hogwarts and learning magic alongside wizardry students. They could use their bending skills in magical duels.
Perhaps the Akatsuki from Naruto somehow get involved in the Avatar world's politics. Their goals of collecting tailed beasts could be translated into a search for some powerful Avatar - related artifacts. This would stir up a lot of chaos in the Avatar world and force the Avatar and his friends to team up with some Naruto characters to stop them.
One idea could be that Gaara, with his sand - controlling abilities, arrives in the Avatar world during a time of great turmoil. He could team up with Aang and use his sand to help in battles against the Fire Nation. Maybe his sand could also be used in creative ways to counter the bending of the various elements in the Avatar universe.
One idea could be that Ben Tennyson's Omnitrix malfunctions while he's in the Avatar world. So, instead of transforming into his usual aliens, he starts taking on the forms of Avatar creatures. For example, he might turn into a flying bison or a waterbender - like spirit. This would create all kinds of chaos and new adventures as he tries to figure out how to control these new forms and also deal with the political and elemental challenges of the Avatar world.
Perhaps the nine - tailed fox in Naruto and the Avatar state could have some sort of connection. In the fanfiction, the two powers could interact in unexpected ways. For example, when Naruto enters his nine - tailed fox mode, Aang's Avatar state could be affected, or vice versa. They might have to learn to control these interactions to save both their worlds from a dark force that wants to use this power connection for evil.
One idea could be a Spartan from Halo ending up on Pandora. Maybe they team up with the Na'vi to fight off a common enemy, like a new type of alien that's more powerful and dangerous than the Covenant or the RDA. The Spartan could introduce advanced human technology to the Na'vi, which would change their way of life in some aspects. For example, they could use some of the shielding technology to protect their homes. Another plot could involve the transfer of consciousness, like in Avatar, but with a Halo - related twist. Perhaps a character's mind is transferred into an enhanced alien body, similar to the Elites in Halo.
One idea could be a crossover with the Harry Potter universe. The Avatar characters could attend Hogwarts and learn magic while also using their bending abilities. For example, Aang could use his airbending to enhance his flying on a broomstick. Another idea is a crossover with the Star Wars galaxy. The benders could be like Jedis, using the Force which is somewhat similar to bending the elements. They could help the Rebels in their fight against the Empire.
One idea could be a crossover with 'Harry Potter'. The Avatar could visit Hogwarts and learn about magic there. Maybe Aang could teach the students about bending while learning about spells himself. Another idea is a crossover with 'Lord of the Rings'. The airbenders could fly over Middle - earth and help in the fight against Sauron. They could use their bending skills to create distractions or help in battles.
How about a crossover with Jurassic Park? Scientists from the Avatar world could visit Isla Nublar or a similar place. They might study the dinosaurs and compare them to the unique creatures on Pandora. There could be a plot where they have to work together to stop a dangerous hybrid creature created from both worlds.
One idea could be to have the Voltron pilots end up in the Avatar world. They could learn bending techniques and use their Voltron skills in combination with them. For example, Keith's swordsmanship might blend well with waterbending moves in a fight.
One idea could be a crossover with another popular fantasy world like 'Harry Potter'. Korra could end up at Hogwarts and have to deal with magic in a completely new way. Maybe she'd use her bending to enhance or counter some spells.