I have! I'm in the process of writing a multi-chapter story for the anime RWBY, and I've done several one-shots for it as well. I also dabbled a bit in Doctor Who. I spent a really long time just reading fanfiction rather than writing it myself because I could never wrap my head around characters that were made by someone else.
However now that I've started writing my own, I find that writing fanfiction is actually an amazing way to practice storytelling in general!
You can practice outlining, character development, plotting out character developments, scene placement, setting, transitions, the whole thing! Fanfiction gives you anything and everything that you need to learn to captivate an audience, while also providing the skeleton of a world that already exists, along with either fully formed characters or just half formed characters that you can flesh out into full ones.
I'm an avid advocate for fanfiction writers and people looking to expand their storytelling skills. That's primarily the reason I decided to write a fanfiction in the first place, was to get general practice for plot development, because laying out a plot is my weakest link in writing. I've had amazing success so far, so if you're ever looking to start writing fanfiction, I cannot stress this enough. Do it!