Pun 101

When talking about context, I couldn't help but think of puns. Let me start off by saying that there are a lot of theories about why funny things are funny. What I'm focusing here is puns, which is just a subset of all things funny (or lame -- depends) and what role context plays. Again, language and philosophy hand-in-hand.
Puns basically makes use of ambiguity. This is where context comes into play. If you remember about ambiguity between lambda and rù (λ), you will see that we need to choose the right context to ascertain meaning. What makes puns humorous is the confusion of this choice of contexts. let's have an example:

There are 10 kinds of people in the world: those who understand binary and those who don't.

Now, the quote says exactly what it says: if you don't understand binary, you won't get the joke; the joke is on you. Of course, the first time reading this you will establish a context, like it or not (since we already argued earlier that for something to have a meaning, it has to rest on a context plane). Well, the context that we established is that "10" is ten, in base ten, as is commonly the case. The pun here confuses the context of base ten and to understand the quote we have to change our context to base two, as hinted ("binary"). Ah, now it makes sense -- "10" is actually two if we convert it to base ten.
Most theorists agree that this unsuspecting element is one of the core elements of all things funny. So: several contexts exist, we chose the most likely one, but oh no, actually it is the other context. This "oh no" part is the surprise element, the unexpected, making connections between contexts that are previously not usually thought to be connected. Daniel Dennet argued that as a reward for making this connection, we fall into fit of laughter. This is certainly an interesting theory since laughter has been proven to have physiological benefits, so it is not far-fetched to call it a reward. I would like very much to address the many theories of humour, but that is another story.
Let's have another pun:

When Mozart passed away, he was buried in a churchyard. A couple days later, the town drunk was walking through the cemetery and heard some strange noise coming from the area where Mozart was buried.
Terrified, the drunk ran and got the town magistrate to come and listen to it.
When the magistrate arrived, he bent his ear to the grave, listened for a moment, and said, "Ah, yes, that's Mozart's Ninth Symphony, being played backwards."
He listened a while longer, and said, "There's the Eighth Symphony, and it's backwards, too. Most puzzling."
So the magistrate kept listening; "There's the Seventh... the Sixth... the Fifth..." Suddenly the realization of what was happening dawned on the magistrate; he stood up and announced to the crowd that had gathered in the cemetery, "My fellow citizens, there's nothing to worry about. It's just Mozart decomposing."

You can immediately see that the punchline is the two meanings of "decomposing": rotting away and the opposite of composing a symphony. It should be noted that the contexts surrounding the two meanings are not really confused -- more like they are fused. Of course the correct course of nature is for a human to rot away in a grave, but a strange phenomenon happened: the backward playing of Mozart's works; both ultimately point to the word "decomposing".
In this light, you can see that rebus puzzles are a kind of pun, too.
Here are few examples (source):Mouseover for answers. Again, there are two meanings, those represented by the arrangement of the visual cues on the puzzle and the other is a common phrase/sentence -- both should point to the same phrase/sentence. Do you see it?
Now, let's talk about categorisation. Language is not only spoken, but written; so it should be no surprise that besides homonymic puns, there are homophonic ones. Homonyms are words with the same spelling but different meanings, like "decomposing". Homophones are words that sound the same but are spelt differently. Example for a homophonic pun:

A: What is the difference between a prince and a ball?
B: A prince is heir to the throne; a ball is thrown to the air.

Needless to say, this is about the similar pronunciations between "heir" and "air" as well as between"throne" and "thrown". There are several other categorisation, such as the rebus puzzle case, in which the arrangement of the visual cues are not really "words", so it cannot be categorised under homonymic -- but in principle, puns revolve around ambiguity of meanings -- this can arise from the same spelling, the same sound, etc.
On a related note, there is a category of homophonic puns called mondegreens. Perhaps they should not be called puns, because mostly, they are not intended. Basically a mondegreen is a misinterpretation of a line because it sounds similar to something else. Sylvia Wright proposed this term because as a child she hear a poem which has a line "And laid him on the green" but she misinterpreted it as "And Lady Mondegreen". So you can see that Mondegreen itself is a mondegreen (this is kind of recursive, isn't it?). I can recall a recent example, which perhaps should be called reverse mondegreen or intended mondegreen. In other words, it's a genuine pun. Language Log dubbed it the worst pun of all time, even. Here it is:

Lastly, let's have puns about puns that I shamelessly plagiarise from Wikipedia:

"The pun is mightier than the word." — original source unknown
(Pun and word: plays on "pen" and "sword", in the saying "The pen is mightier than the sword".)
"A pun is its own reword." — Dance Drier, British comedian
(Reword: pun on "reward", from the saying "Virtue is its own reward".)
"Hanging is too good for a man who makes puns; he should be drawn and quoted." — Fred Allen
(Quoted: pun on "quartered", an old form of capital punishment.)
"Immanuel doesn't pun; he Kant." — Oscar Wilde
(Kant: play on "can't", in the name of philosopher Immanuel Kant)

So punny.