1. Stories Have to be About People
One of the biggest things about fan fiction that I've seen is that the stories many times don't deal with people. The story is about a machine, or a plot device, or about a caricature of a person. I'm not saying stories about things instead of people don't do well or can't do well. Gundam is INHO way more about the mecha than any of the cast members. The machines are sometimes much more memorable. Starship Troopers is the same way, in the novel we learn really nothing about Rico, and the book is just a novel length bit of political editiorializing wrapped in speculative fiction. What you write, if you want it to be successful has to be about people. Titanic is a tragedy, a love story that just happens to be set on the HMS Titanic. Star Wars isn't about X-Wings and light sabers, it about the heroes journey and how Luke becomes a Jedi and then how Anakin becomes a Sith. So write about people. Real people.
2. Do Your Homework
A common gripe of mine, there is a good deal of fantasy and science fiction where the writers simply didn't do their homework and they handwaved everything to cover up the fact that they didn't put in the due diligences to make sure their stuff was solid. There are so many futuristic and war novels and settings where the gear the characters use is not subpar by our modern standards, but subpar by our grandfather's technological standards. Battletech is a horrible offender in this manner, as are the tropes of katanas cut everything and my sword beats your gun. The same thing can be said of fantasy, you don't have to have a degree in medieval demographics and anthropology, but a little homework can go a long way.
3. Not All Bad Guys Are Bad Guys
Keep your villains sympathetic. Frankenstein's Monster was a victim of it's creator's madness, Dracula was tormented by lost love, and the Wolf man was never fully in control of himself, he was at the mercy of the beast within. The Baddies need to be baddies because they have a different set of values and an agenda contrary to the good guys. The baddie for the sake of being a baddie is a limited caricature, and Shakespear pulled it off with Richard III because the titular character decided to be a baddie because he was unhappy with his lot and the happiness of his contemporaries. The villain doesnt want to destroy the world, it is just a step in his plan to remake the world in his liking, say with his deceased wife restored to life (this is pretty much the core story of Neon Genesis Evangelion) Gendo Ikari is going to annihiliate the world so it can be remade where his wife wasn't devoured by one of evangelions.
4. Not All Good Guys are Good Guys
This is a harder rule to work with because it is so easy to just accept the vanilla hero as a contrast to the chocolate villain. Heroes need motivation to do the things they do. The term anti-hero is bandied about, but all too often this comes across as a jerk ass hero, rather than a neutral character who does good things but for the wrong reasons, or does bad things for the right reason. Luke Skywalker is the epitome of the vanilla hero, your aunt and uncle are dead, the empire wants you dead, your home has been destroyed, way to let goof your old life. Han Solo is a thief, smuggler, con man and general scoundrel and he ends up doing good things, but out of interest for preserving his own hide, not the good of the rebellion or the galaxy. Good guys need their own flaws to keep them from becoming shining do-gooders. Sam Winchester becomes addicted to demon blood (and probably some demon nookie) Dean Winchester is an unapologetic womanizer. Mal Reynolds is a smuggler, and Doctor Who has to deal with hubris and grappling with his pacifistic way of compulsive interference.
If you can't sum up you plot in one or two sentences, it either needs work, or you don't have a plot. Two brothers resolve family issues while hunting cryptid (Supernatural) A band of unlikely comrades face challenges while traveling on a ship (Star Wars, Firefly, The Odyssey, Farscape, Andromeda, Star Trek). There are in truth very few true stories, accept this and move on. Avoid the cliches, and take something that is timeless and make it your own. Add twists, add unexpected endings, don't be too predictable but don't blindside the reader. Leave a faint trail of breadcrumbs, but stay out of Acme Acres if that makes sense.
6. Kill Your Darlings
It is easy to become infatuated with out own creations, and in doing so we can start projecting ourselves (author avatars) or our desires (Mary Sue) into these characters. Both of these are generally frowned upon. Don't be afraid to nerf a character you've become too fond of, or be aware of your personal emotional involvement with the character. Don't write something about being a writer, thanks ahead there. Harrison Ford wanted Han Solo to die heroically in Star Wars, Rambo died in the end of the first book. People die all the time, don't be afraid to do the same to people who aren't real.
7. Good Artist Borrow, Great Artists Steal ~ Scrasamax
This is not an endorsement for plaigarism but rather pointing out that there is nothing wrong with taking material for other sources and using them for your own ends. You can write about a very dead pan straight laced person of authority who believes in a fringe theory, and their skeptical foil and have sexual tension between them without writing about Agent Mox Fulder and Agent Sana Dkulley. Strip away the flash and greebling and find out what it is about the thing you like that is the thing you like. Supernatural works because it is based around the relationship shared between brothers, the X-Files balanced sexual tension (Gillian Anderson :swoon:) and UFO cryptozoology and conspiracy theory. Individually the characters in Lost were unremarkable, but mix them together and they become a savory stew and once the endless litany of keywords, arc words, and unexplainable mysteries were dropped in the show was a hit.