It's such a huge fandom that anything you think is universal will have people against it. With five series and ten movies, odds are you'll find people who hate or love any number of them. Semi-universal, though:
-(The Original Series) Kirk and Spock. Whether you slash or not, you still probably believe that their friendship is sacred. To some extent, the friendship of Kirk, Spock, and McCoy is regarded the same way, but since there aren't as many people who support a threesome it doesn't have quite the support of Kirk and Spock.
- (Voyager) Janeway/Chakotay over canonical Chakotay/Seven. There re some C/7 shippers, but they are in the minority. Very much so.
- (Voyager) "Threshold" isn't canon. Even the writers say so. Can't blame them - what show wants an episode where two of the main characters superevolve into mutant lizards and have mutant alien lizard babies?
- (The Next Generation) **SPOILER ALERT** Much of the fanbase (not all but a significant enough portion to put here) believes that Data didn't die in Star Trek: Nemesis. To be fair, there are a lot of hints of his return, and maybe he would have if Nemesis hadn't been a box office flop and therefore closed the door on Star Trek movies until the 2009 reboot. (Strangely enough, Data's death may have caused the movie to flop, seeing as he's a fan favorite.) Fanfiction abounds explaining his return or simply ignoring the issue. I myself have written a fic doing the former.
- (Voyager) A vast majority of fans agree that the last episode of Voyager didn't resolve everything, or at least, that there is potential for stories after it, to the point where seeing fanfiction tagged "Post Endgame" is like finding a Suefic in the LOTR archive.

You probably didn't read much of that unless you know Trek, but yeah, that's what I can think of. I think the reason Voyager has so much is because while it was excellent, it was plothole-ish, leading the fans to fill the plotholes.

(end Trek gush)

You can have a moment when a character one-ups Sherlock for a moment or two, but you must never ever ever have a character naturally smarter than him who isn't Mycroft, Moriarty, or Irene.

Because generally if you've an OC that can do that, people scream Mary Sue. And they're usually correct (seriously, Suethors, find a better character template for your OC than Sherlock bloody Holmes I beg of you).

Aside from that, no other rules really come to mind, because most rules that I know are just fanon that have cemented themselves into the collective psyches of the fandoms I'm a part of.

Oh, there's the THOU SHALT COUNT TO NINE stuff for the LotR fandom, but even in some instances that could be waived for a very amusing story or two.

In all seriousness, though, I think you would be amazed how truly unforgiving the Kingdom Hearts fandom can get over such things as not knowing the confusing-like-an-Escher-painting story.

And then there's the really radical FF7 fans who won't even let you say the first syllable of Cloud/Tifa, Cloud/Aerith, or Cloud/Yuffie (depending on which end of the ship spectrum they're from) without destroying you.

Oh yeah, and good luck trying to show some rather perverted Tales Series fans that you aren't insane for not liking the Ms. Fanservice character because she's a total b*tch.

Ugh. This is why I just play the games and stay right out of the fandom world most of the time.

I've never encountered things like that before, but then I try to distance myself from anyone who might screech about broken rules of fandom. There is a difference between politely asking for someone farther along in the story than you not to spoil the parts you don't know and shrieking "DON'T SPOIL ANYTHING THERE MIGHT BE PEOPLE WHO DON'T KNOW ABOUT THIS YET" every time others try to discuss something like civilized human beings, so I generally run with people of the same fandom who will stick a NORMAL spoiler warning (as opposed to !!!!!!!!!!!!!!!!!!!!!!!!!!!!!SPOILERSOMG!!!!!!!!!!!!!!!!!!!!!!!!!!!!) on posts with spoilers, but leave it at that. The same rule applies with other fandom rules.

I dunno, I don't do well with people becoming rabid over fictional stories/video games/etc. It doesn't make much sense to me unless the canon in question is being mangled rather than speculated upon or added to in an affectionate manner - and even then, a whisper can go much farther than a banshee wail.

That said, there's a growing group of Wrathion/Anduin shippers in the World of Warcraft fandom, and with it is an equally growing group of "EW OMG WHY" anti-shippers. It's kind of amusing to watch the rampaging ship wars, but I'm staying out of it.