I've written for myself, my own stories but for fanficiton, I've written one [http://www.fanfiction.net/s/8299583/1/Tide-Lords-Fanfic]... well actually four chapters of one with more to follow. It features the characters of Jennifer Fallon's "The Tide Lords" series of books of which I am a big fan. Fallon is an incredible author, the series particularly brilliant and the characters were cool...but the series ended and I *had* to know what happened next.
I've re-read it a couple of times over the years and each time I've looked straight after for a fanfic and never once came across what I was hoping for. So, in the end I figured I would just have to write it myself. I'm a very good writer but writing someone else's characters is hard. I began by asking "what happened next" and decided to follow on immediately from the end of the actual story...with a tiny nod (by way of an homage) to an unofficial/non-canon short story she herself wrote called "The Magic Word".
To the OP, if you want to write, write. It doesn't have to be a fanfic, but if you have an idea, work on it. It doesn't have to be a novel, an essay or even a short. Even a single scene, or conversation is good practice. Sometimes a well written non-canon story can be as good or better than the original work as there's infinite creative freedom. The best ones keep the tone of the original work and the characters consistent and have good grammar, punctuation and spelling.