This is old, and rather well-known in some circles:
'I didn't say she stole my money.'
This sentence has seven different meanings – depending on which word you stress.
There's a famous headline in the history of the British print press, which I quite like:
In the mid-Eighties, Michael Foot, a former Labour Party leader, was appointed chairman of a nuclear disarmament committee. The Times reacted with this headline:
'Foot Heads Arms Body'.
It's been disputed, but a sub-editor has confirmed it a few times.
Since the question doesn't specifically mention English sentences, I'd like to mention a Sanskrit poem which is filled with linguistic ingenuity: Shishupala Vadha by Magha.
I'm quoting directly from Wikipedia here, so all credits go to the authors of the Wiki article.
The 66th stanza of the poem has only two consonants and makes a perfectly sensible couplet.
"The fearless elephant, who was like a burden to the earth because of its weight, whose sound was like a kettle-drum, and who was like a dark cloud, attacked the enemy elephant."
Sreeram N Ramasubramanian
'I do not know where family doctors acquired illegibly perplexing handwriting; nevertheless, extraordinary pharmaceutical intellectuality, counterbalancing indecipherability, transcendentalises intercommunications' incomprehensibleness."
(From Dmitri Borgmann, 'Language on Vacation: An Olio of Orthographical Oddities', 1965)
This is a 'rhopalic' sentence: a sentence or a line of poetry in which each word contains one letter, or one syllable, more than the previous word.
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