There's this thing called fanfiction, wherein an amateur author writes a story using the characters from their favorite books, TV shows, etc. and then publishes them online. It's generally considered a form of flattery, doesn't make much money, and thus, isn't penalized under copyright law, even though it technically should be. Sometimes, that fanfiction develops into something else - the Random House bestseller Fifty Shades of Grey (as of this posting, the book is over on the Amazon's Most Wished For list in the sidebar) started life as a Twilight fanfiction.
There's also this great internet meme called "shipping" (a derivative of relationship), wherein fans of a particular show or book or comic wish for a particular relationship that doesn't quite exist in that world's reality. For example, people might ship Wolverine and Storm, Heathcliff and Nelly Dean, or there's even something called Wincest, the pairing of Supernatural's Winchester brothers, Sam and Dean.
Write a fanfiction story in which you ship a pair of characters that are normally not paired up. Then change the names and setting to create an original work.
Imitation is the finest form of flattery, people.