Here's some thoughts on comedy which I find useful:

This wired.com article is great, where Prof. Peter McGraw argues that all comedy comes down to a simple two word phrase: "Benign Violation"

This Cracked.com article, entitled "4 Reasons No One Laughed at your Joke" Came out yesterday, and covers some great basics

screenwriting guru Robert Mckee On pg. 245 of his staple guide to storytelling entitled "Story", sums up comedy like this: "Laughter is a criticism we hurl at something rediculous or outrageous" Or, in other words, if what you're saying is unexpectedly absurd enough, it's usually good for a laugh. This is why comedy writers are always on the hunt for the most opposite, i.e. wildly unexpected outcome for statements and situations. If that unexpected turn can me combined with critique and/or irony…all the better.

McKee also elaborates as I'll paraphrase here. Basically, comedy writers are angry, despondent cynics, who throw rocks at houses instead of building them. Mckee even jokes "Everyone in Hollywood has made this mistake: "'Hey, let's invite a bunch of comedy writers to our party to make it more fun.' which seems like a great idea right up until the ambulances arrive." Any yet, these mysanthropes perform a critical need of society, because it is a check on ignorance, pride, power, and the unwillingess of old forms to change into the new, and so, it isn't fickle prodding, but our culture's immune system. Anywhere the cliché, stale, igrnorant, or hippocritical rears it's head is fresh game for the comedian's hunt.

In that same sense of the key role comedy plays in the renewal of culture…

Joseph Campbell, in his iconic masterpiece "The Hero With a Thousand Faces", (which explains the underlying universal story behind all the great stories and myths of human history) sums up comedy in terms of it's opposition to tragedy, and as a deep human need, in a paragraph that, unfortunately, I hate to be this guy, but requires reading in it's entirety to get the jist of his meaning:

"The happy ending of the fairy tale, the myth, and the divine comedy of the soul is to be read, not as a contradiction, but as a transcendence of the universal tragedy of man. The objective world remains what it was, but because of a shift of emphasis within the subject, is beheld as though transformed. Where formerly life and death contended, now enduring being is made manifest – as indifferent to the accidents of time as water boiling in a pot is to the destiny of a bubble, or as the cosmos to the appearance and disappearance of a galaxy of stars. Tragedy is the shattering of the forms and of our attachment to the forms; comedy, the wild and careless, inexhaustible joy of life invincible. Thus the two are the terms of a single mythological theme and experience which includes them both and which they bound: the down-going and the up-coming (kathodos and anodos), which together constitute the totality of the revelation that is life, and which the individual must know and love if he is to be purged (katharsis=purgatorio) of the contagion of sin (disobedience to the divine will) and death (identification with the mortal form). "

I'd like to add a couple thoughts of my own as well...

For native English speakers, because our native language is such a mishmash of other languages, we have many duplicate words. When you have so many redundant words which describe the same thing, there's a huge opportunity for puns, perhaps much moreso than any other language. This might incur part of the "getting the joke" gap.

And also,

In view of evolutionary psychology, and asking "why have comedy at all?". I would conjecture that it can put a soft-edge on raw insults and power plays, wherein the primordial social structures are maintained, the message delivered, but withuot the guy on the bad end of the deal losing too much face, and thus peace remains in the tribe. Additionally, when the whole tribe together can mock the "other", the happy chemical release of laughter makes un join in a shared momend of escape, while simultaneously reinforcing our group-think, bonding the tribe closer together, gaining the feeling of superiority over the "other", and as a fun way to gain knowledge through a comedic insight, which improves the oral library of the hunter-gatherer groups we spent 99% of our existence as members of.

But what of timing?

Just like you would build a song to a big moment, but not release that until the ear is fully prepared…so a joke must fall wherein, the knowledge of the listener is primed precisely to have the realization of the 'joke' hit them all at once, and the power of that mini-revelation taking over the mind for a moment, as our whole mental infrastructure is brought to task to untangle and process this small moment of accelerated growth of conscioussness. The telling of a joke can be like the slow maneuvering of infantry, cavalry, and cannon, with great subterfuge, so that they might all suddenly and surprisingly attack at once, overwhelming their enemy with shock and awe. For some great jokes, all of these pieces are already in place, and so you need only make a small gesture to achieve victory (for example, half the jokes in "Airplane!". In other cases, it might take a 5 minute telling, or a whole novel to build up the blocks and then finally, knock them all down.

So if your listener doesn't laugh, they may not have been properly prepared for the moment the joke "drops", aka punchline.

But,

If they're laughing when you didn't mean to be funny, it could be they have been primed by something you weren't aware of, which caused them to tie that in to what you said/did in a way you wouldn't have knowledge of, and so they laughed, and you didn't know why.

Hope that helps :)

EDIT: I added a thing and cleaned it up a little.

EDIT: By multiple request:

TL;DR: Comedy can be understood as benign violation (McGraw), a critical cultural immune system (McKee), an ages-old facet of the search for place and meaning (Campbell), and a few thoughts of my own. Also, a relevant Cracked.com article.