I'm feeling chatty this week (well, chatty for me, which may still count as taciturn) so I'm going to go ahead and offer to do the Character Interview meme. If you have any questions for any of the characters in any of my stories -- all 5.5 years worth -- fire away and I will see to it that they answer you.
Whilst I've been reading lately, both HP badfic and SG-1 goodfic, and trying to gear up for writing some SG-1, I've been thinking about how people get together in fanfic.
IRL, people can hook up in a lot of different ways. They meet through friends, through online services, through mutual interests, etc. They date. They form relationships.
In fanfic, since we're usually pairing up two canon characters, they're normally already working together. And normally, in a situation where it might not be wise to date and very well might be against some sort of regulation. For slash, add that we're dealing with characters who are not generally canonically out as gay or bi.
It's a little different in HP fic, if you're writing about the kids at school. If you want to write Draco/Hermione, you do have to deal with the whole "will looks overcome 5 years of intense hatred?" issue, but still and all, Draco can ask Hermione out. But he can't just ask Harry out, even if the 5 years of intense hatred are somehow worked out.
So, getting two characters together often involves some sort of catalyst. The catalyst doesn't (usually) cause the two to love each other, but it causes them to act on feelings they already have.
(BTW, I'm being serious about this, not mocking. These things can be cliche, but they can be used subtly as well.)
Alcohol or drugs
The classic inhibition lifter. Often combined with other catalysts to smooth the way, but sometimes used on its own for a good, old-fashioned drunken screw.
One of the characters has some sort of strong experience, like dying and coming back. (I won't even try to start listing all the characters that's happened to.) Or getting transferred. Or having a loved one die (and not come back). An old girlfriend comes to town, etc. The stress of the changes makes either of the two act on their feelings, where they weren't before.
This is the magic, alien technology, experimental drug, etc, that forces the characters into an awkward situation where they are closer than they might otherwise have been. Maybe they can read each other's thoughts now. Often, their secrets are revealed, and thus, their feelings.
Character C suggests that perhaps Character A needs to tell Character B how Character A feels about Character B. Most usually the province of Mary Sues and Token Female Characters, but sometimes Dumbledore has this function as well.
Can't fight this feeling
The lust/love/Force is so strong that the characters just can't stop themselves. Works well with alcohol.
Circumstances beyond their control
For reasons of health, diplomacy, or the safety of the entire universe, the characters must pretend to be a couple, must kiss, must shag, sometimes in public. This can lead to discovering that they like it.
The big fight
One of my favourites, usually used only in slash (big exception for canon Buffy/Spike). Two characters express their aggression in a knock-down, drag-out fight which then turns into knock-down, drag-out sex. Yum.
Have I missed any? I'm sure there are lots of variations particular to each fandom.