The buffalo of Buffalo are notorious for their buffaloing of other Buffalo buffalo. It's a self-perpetuating cycle of intimidation, so the Buffalo buffalo Buffalo buffalo buffalo themselves buffalo Buffalo buffalo. It's tragic, really.
Hannah Werdmuller's wonderful London Zoo includes the line
'Do the buffalo buffalo buffalo buffalo buffalo buffalo? And if so why can't they just get along?'
You might like to play this as a soundtrack while you read the rest of this writeup.
I first came across the Infinite Buffalo Effect in Steven Pinker's flawed but fascinating The Language Instinct*. It is actually possible to construct an arbitrarily long sentence in English using only the word buffalo**, even without involving the city in upstate New York; 'buffalo buffalo buffalo buffalo buffalo,' for example, means 'the buffalo buffaloed by buffalo in turn buffalo other buffalo'. To buffalo is to overawe, bewilder or intimidate, so we could rewrite that as 'bison bison bewilder bewilder bison', which is only moderately difficult to parse. Similarly, "buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" means 'the buffalo buffaloed by buffaloes from Buffalo themselves buffalo the buffalo of Buffalo.' Do you see?
'Buffalo' is part of a small class of English words which can be both plural nouns and transitive verbs, and which in principle can be used (together or separately) to construct grammatically correct sentences of any length - although only some of them really make sense. See my Buffalo Generator for arbitrarily many examples of these in action. I'm going to attack these roughly in order of ascending plausibility:
This one is perhaps cheating in that it is only a homophone, not a homograph - and in some accents, not even that. If we allow it, though, it has the bonus that we can choose between at least two different and grammatically distinct meanings. I bet that boar do bore boar - I'm sure I'd get sick of the company of pigs sooner or later - and of course, boar bear boar when they're pregnant.
Another homophone-only pairing. Plaice wouldn't normally place plaice, but maybe they would if they were lining up a school photo or something.
Fish fish fish
To me, this is unconvincing: In my dialect of English, you can't just fish something without a preposition, you need to make it a phrasal verb. You might fish a dead body out when you are fishing in the lake for halibut, but if you said you were going to 'fish the creek', you'd be speaking a different kind of English from me. Nothing personal.
Bream bream bream
It turns out that to bream is 'To clean, as a ship's bottom of adherent shells, seaweed, etc., by the application of fire and scraping.' I guess it's not impossible to imagine a world where bream do that to each other.
Char char char
Similarly it's not too hard to see fishes of the genus Salvelinus scorching each other, given access to sufficiently powerful flamethrowers. Or laser beams. As far as I know this is the only Infinite Homonymic Sentence that is also a kind of dance.
Perch perch perch
For perch to perch perch would require a degree of acrobatic imagination that perch are not known to possess, but at least it wouldn't call for any advanced weaponry to be specially modified for ichthyic use. Don't ask me why so many of these have to do with fish.
Dice dice dice
I'm enjoying the image of knife-wielding dice chopping each other into ever-smaller cubes. I might make an animation of that, or possibly even a computer game.
Pants pants pants
I doubt if any real pants have ever pantsed other pants, but if they did, that would be a pants thing to do. Only pants pants pants pants. This is one of only two words I know that are adjectives as well as transitive verbs and plural nouns. For anyone who is lost at this point, 'pants' as an adjective is a British colloquialism meaning 'rubbish'. The OED defines the verb as 'To pull down or remove the trousers (and sometimes underpants) of (a person), esp. as a practical joke.'
People people people
Multiple personality disorder could be said to be an instance of people peopling people. Or those imitation people from Doctor Who which are actually live-in vehicles housing lots of little tiny humans.
Cod cod cod
To cod someone is to hoax or parody them. I can totally see cod doing that. They're not as stupid as they look. I'll bow to wertperch's superior pescapsychological knowledge here though: 'Cod are actually much nicer than that', he informs me. 'Cod' is also an adjective meaning 'sham'. Meanwhile, the kodkod is a small wild cat found in parts of Chile and Argentina, like a tiny leopard. Even if cod wouldn't cod cod, I bet they'd cod a kodkod, given half a chance.
Smelt smelt smelt
In British English, 'smelt' is the standard past tense of 'smell', and it's definitely true that salmonoid fishes of the genus Osmerus have smelled other smelt-fish. Fish often rely on their sense of smell, even though they don't have noses. It is also possible to imagine circumstances in which they might melt or fuse other smelt, perhaps because somebody has summoned an army of self-repairing fish-golems. In that case it would likely turn out that smelt smelt smelt smelt smelt: Smelt-fish smelled by smelt-fish meld smelt-fish. Someone with a bit of time on their hands could probably write a formula for how many of the smelts among a sentence of N repeats can legally be one or the other, given the mixed tenses; it's not obvious.
Police police police
This is frequently true, and dangerously so! Too often we let police police themselves. Still more dangerous is when we let the police police police police police. It is hard to safeguard against, but somewhere the chain must be broken, if we do not want to live in a police state!
I wonder if that's everything?
* Steven Pinker attributes this observation to his student Annie Senghas. The computer scientist Bill Rapaport is certain he came up with it earlier (along with variations having to do with the buffalo of Buffalo doing the Buffalo buffalo, imagined to be a bit like a more bisony version of the Tennessee Waltz); the earliest known printed reference to buffalo-only sentences appears in Dmitri A. Borgmann's Beyond Language--Adventures in Word and Thought (1967).
** I hadn't fully appreciated this till conform pointed it out, elsewhere in this node.
Andy Glowaski and Neil James Rhind have been particularly helpful in coming up with examples. I have also drawn on, and contributed to, this Wikipedia Talk page.