What is the best part about writing fanfiction?

The best part, is that you can have the characters do things they would never get away with in a tv show or movie. 

You can have highly improbable romances......or even have characters commit murder, and cover it up. 

You can go where ever your imagination takes you, that tv shows,   would never do. 

Not into smut or fanfiction. It's fun for people and I have no problem with people playing with other people's creations for fun and to get involved in a community. It can lead people to discover their talents. I know a few successful published authors who began writing fanfic because they loved a TV show. I find it really hard to write about things created by other people so have never done it. 

I'm not into smut and would not do that to anyone's characters. If you like to smut your OCs, or if the canonical characters were into that, ok. Everyone has his own tastes.

I like musing over what makes those canon characters so special to me, or what I would do if I were the characters, or how would they solve my problem.  For instance, an auld acquaintance of mine wrote a novellette in which Sherlock Holmes and Irene Adler solved an auld and unsolved missing person's case "The Disappearance of Theatre Magnate Ambrose Small" (It is a true-life mystery that occurred in December 1919.) I confess I was picky about points, but the overall story was clever, with a good nasty villain who nearly gets Holmes and the clues are well mingled. Holmes, Watson and Irene were much like Doctor Doyle prescribed, though I think Irene was capable of more than my friend gave her.  I would have told my own version. James told his and I honour him for it.

Many, many adults write fanfic, including people who've got published books out there. It's fun, there's a community of fans who seek it, and as long as the rights owner doesn't go after such writers for copyright violation (which it is), it does no harm. Publishers, movie and TV studios, the actors who play the characters, etc. have come down on the side of allowing it, with very few exceptions. All publicity is good publicity.

The best fanfic writers I know are published authors, mostly not in romance but other genres. They think it's fun to write new ships with existing characters, following canon of the source material. And because they don't have to create the character or the environment/situation/world in which they live, the writing's easier than it might otherwise be.

A lot of fanfic creates romantic or sexual pairings that do not exist in the original work. When it's well written, the romance can shine, and the sex scenes can be especially hot because the reader can envision the characters even if they're light on description.

Well, I suppose you can write improbable things, like a naked Mr Spock.  But then, I'm not a teenage girl and never have been.