I don't read any, but I think they pretty cool. People expressing themselves with the culture they consume is the way humanity have created culture for thousands of years until copyright laws where invented.
Fanfiction isn't a monolithic homogenous entity. Some of the most entertaining, well written stories that expand on their respective narrative universe are works of fan fiction but there are also poorly written abominations that cause psychic damage just being read.
One thing I love about fanfic is that it's a shortcut to storytelling. So, like, you pick up a new novel, not part of a series or anything, and you start to read. And you have to map out the entire milieu in your brain: these are the main characters, these are their relationships, this is their backstory, these are the things you need to remember about the location or politics or whatever else there is.
You spend all this time absorbing all this information and learning to really care about the characters and following events as they unfold and then -- it just ends. And then you pick up another story and you have to do the whole thing all over again.
The nice thing about fanfic is that you can skip all the universe-setting stuff: you can (generally) assume that a reader will know the characters, relationships, back stories, etc etc etc. You can literally start a story with the line "Dudley chased Harry down the street" and not have to explain who Harry is, who Dudley is, why Dudley is chasing Harry, why Harry can't avoid or hide from Dudley's attention, why Harry's best option is to run, vaguely how old Harry and Dudley are, why Harry can't get someone to help him - hell, you even know it's summertime. Fanfic is a shortcut to storytelling, enabling both the reader and the writer to get to the meat of the story without (necessarily) needing to faff about explaining and trying to remember all sorts of details.
I have often described fanfic as the mythology and folklore of the modern world. Captain Kirk is the equivalent of what Hercules was to the ancient Greeks, a hero that everyone knows about and so can be an archetypal hero in anyone's story.
Copyright is a very unnatural imposition on how this aspect of human culture has worked throughout the vast majority of history. It really annoys me when people discuss what elements of a setting are "canon" and fall back on the authority of the legal system, rather than what the collective will of the fandom feels is the correct course of things. Imagine if someone had "owned" Poseidon and had suppressed the Iliad because Homer was doing unauthorized things with the character.
I would argue that the "owner" of the mythology does have a stake in keeping the stories "authentic". In those ancient days, sure there was no copyright, but there was heresy, which was effectively the means by which the writers protected their core IP like Poseidon and Zeus, the Bible and Gospels etc. Otherwise these stories would not have survived the millenia mostly unaltered.
Take Poseidon's trident away and give him a sword and people aren't going to be impressed. They might even kick your ass as Poseidon was supposed to be a real god at the time.
If you wanted to write non-canon fic back then, you made your own in-universe characters like Odesseus or Hercules and if you were lucky, they became adopted as part of the Greek Mythology expanded universe. But you had better write the gods as they were intended, or you could be exiled or worse!
Likewise today, a world like Star Trek has in-universe rules that you can't break or else your fic becomes non-canon, and you may be mocked or "exiled" from the community.
Take Poseidon’s trident away and give him a sword and people aren’t going to be impressed.
But the point is that it's the people who aren't going to be impressed. Not some random "rights holder" that has that title only due to an arbitrary shuffling of tokens of value that happened out of sight in some hidden office or courtroom. Churches may try to declare particular ideas to be heretical, but if the general populace goes against those declarations they quickly change their tune or get schismed.
If someone back in ancient Greece had somehow "bought the rights" to Poseidon and decided that from now on he'd wield a sword (so that he can sell Poseidon-branded swords or something), he'd have been ignored. People would keep telling tales of Poseidon's trident, and the tales with the sword would just vanish into irrelevance because nobody would retell them.
Having seen things much like this happen to a number of franchises I've loved since childhood, I really wish this was still the way of things.
It's like any other writing. Some of it can be good. A majority of it fucking sucks. And some of those things that suck become good because they suck in the right way that they become funny, like Full-Life Consequences and other internet meme fanfics.
Since there is no publishing barriers you end up with a lot of bad content that wasn't filtered out from the platform in any way. That's no necessarily bad, it's just harder to find good writing, but it gives novice writers a way to just get out there and get feedback. When you find good stories it's just a way to get more from characters and worlds you want more of.
I specially like slice of life types of stories where you get to peek into the "boring" parts in between the cannon story lines.
There's also generally a lot of smutty content that you can filter out if you don't want to see it.
Like others have said some of it can be shit but you can come across genuinely good writers as well. I don't read it anymore but when I was younger I was really into it. There's one story that was pretty much like the length of a book and being released by the chapter every few weeks or months or whatever and the writing and story had such an impact on me, I still think about it often.
Depends on the fanfiction. There's a lot of good ones out there, but also there is way, way more low tier/low effort stuff written by grade schoolers, so sometimes it feels like you're wading through a sea of oyster mucus to find a pearl.
There was some era where teachers were telling students that the main thing was to get their stuff down on paper and they could work on format later. Which lead to a truly horrendous period where all the newbie writers were releasing stories full of mis-spellings, no punctuation or paragraphs, constantly shifting verbs and POVs, lack of plot, horrible characterization, etc etc etc. Think of every single writing crime you know of, and these stories were full of them.
And you'd very gently write them and suggest maybe punctuation would make it easier to read, or one sentence shouldn't take up two pages, or actually naming the character who was doing or saying something instead of just expecting the reader to pull it telepathically outv of the ether. And they'd get all defensive, "Well it's MY story and everyone else has liked it and doing all that stuff just slows me down and the important thing is just to get the thing down". You'd suggest maybe they could use a beta reader, but no that was too much work as well.
I had to give up on entire (small) fandoms because the writers simply. Could. Not. Write. I'm really glad that era seems to be over.
Even though the work is not completely original, something that the internet has only recently starting lacking is a mass variety of creative writing. This is due to a lot of reasons, yet mainly it's intense moderation policies and increasingly strict advertiser friendly narratives being policed. There was more creative writing online within forums during the early 2000s. Anything that grows creative writing is a win.
Every time the topic of fanfiction comes to mind, I think "I ought to read more of that."
But when I actually try to find some fanfiction to read, I find I have to sift through a veritable mountain of erotic fanfiction to get to anything else. (Nothing wrong with erotic fanfiction, mind you, but it's not really what I have in mind when I think "I ought to read more fanfiction.") Maybe I'm not looking in the right places.
I do think it's on balance a good thing, that more of it ought to exist, and that it should be legal. (It pretty unambiguously isn't legal at least in the U.S., but it should be IMO.)
So: I used to read gen fic. When I talked about fanfic with my fan friends, I always said I liked the characters and the relationships. They continually tried to get me to try slash fic, and I would, I really tried: I'd find stories in the fandoms I was in featuring 'my' pairing and I'd try them ... and honestly, they were crap. I could not believe my fan friends were reading such poor quality stories!!
Then a friend sent me a gen zine for my birthday. It had three big stories in it, two of which were my big fandoms, the third some show I'd never heard of before, but I read the story anyway. And if was fantastic. I immediately wrote everyone I knew asking if they knew of any other stories, and another friend loaned me a different gen zine. Another long story, really really good I immediately decided that I was a fan of this show, the fic was great!
So I wrote my friends again and it was at this point that I found out that, somehow or other, I had managed to read the only two gen stories in the entire fandom - absolutely everything else was slash.
But I loved my new fandom so I decided to "tolerate" the slash - but it was good too!
It was much later, after going through more fandoms than I care to think about, that I realized that for most fandoms (though not all!), but that the really good stories in many fandoms are either mostly slash or mostly gen. So the gen fandoms I loved the fic on - I loved the fic because the good writers in those fandoms were writing gen. And the slash fandoms I got into - I lived the fic there because the good writers were writing slash.
Nowadays I wander freely back and forth, depending on what shows attract my interest. And sometimes I'll be reading gen and sometimes slash, but I end up reading one or the other because that's where the good writers in that fandom are.
Which is a really long-winded way of saying that, maybe it's the fandoms you're in that you're ending up with stories that don't interest you. It does happen!
When it expands on a story/universe and can be considered canon to it, I quite like it. A good example would be Star Wars, which has a great fanfiction community that stays relatively canon. Now, what I do not like, is someone’s twisted fanfic about a sexualized Clifford the big red dog. That is disgusting in my opinion…
If ever I get access to a time machine, I'll go back and introduce the Victorians to the concept. The resulting singularity of godawfulness could power the world for millennia.
While it's legal status might be dubious, from the fiction quality perspective it's no different from non-fanfiction. Like, there's a ton of crappy fan and non-fan fiction alike, and then there's genre-carving stuff like HPMOR that basically gives the original Harry Potter books a purpose and excuse to exist.