That's right. I said it.
I know some people knock fanfiction because it seems silly. And it is. Believe me, I've read my fair share of terrible, completely out-of-character, poorly written fanfictions. But that's the nature of writing, isn't it? I don't know a single person who hasn't read a bad book. The problem is that these stories are unedited and self-uploaded to free sites, so... where's the quality control?
It may be that I have a soft spot for it because my real writing journey (aside from school projects and stories I wrote when I was under twelve) began with fanfiction. For me, it was a great exercise because the characters had already been created for me! And, if there was something I didn't like about the way the author handled a situation or relationship between two characters, I could change it while still staying true to the world and the story they originated from.
Now, don't get me wrong. Fanfictions can go very wrong very quickly, and they're not always a good base to get started for reading them. However, as a writer, writing one provides nearly limitless possibilities. If you're looking for a writing exercise, think about your favorite character from your favorite TV show, whatever it is. Throw them on a deserted island. How would they react? What would they do first?
For me, the hardest part of writing is character creation. You have to think about every aspect of this fictional person's life, as in reality, every aspect of someone is what determines their personality, down to their favorite color. With fanfiction, this is already done for you! Your only job is to create a story. Maybe something great will come out of it, either an idea for your current WIP or an idea for a brand new one!
Let's not forget that Fifty Shades of Grey began as a Twilight fanfiction story.