An overweight lass from Calcutta
One day was heard to mutter
It’s so blasted hot
The sweat from my motte
Is forming large pools in the gutter
She frowned and called him Mr
Because he never kr
And so, in spite
That very night,
This Mr kr sr!
There once was a lady from Worcester
Who ussessed to crow like a roosesster
She ussessed to climb
Two trees at a time,
But her sissister ussessed to boossesster!
There once was a gourmet of Crediton
Who took pate de foie gras and spread it on
A chocolate biscuit
Then murmured, “I’ll risk it!”
His tomb bears the date that he said it on.
I feel as though I should apologize for the cleanliness… 
Well, it’ s not dirty or anything, but it was the first one I learned:
There once was a man from Black Heath
who sat on his set of false teeth.
Cried he, with a start,
Oh Dear! Bless my heart,
I’ve bitten myself underneath!
My dirty-old-army-sergeant-grandpa taught it to me when I was 8. He almost taught me the one about the girl from Nantucket, but my grandma apprehended him first.
There was an old maid from Duluth
Who wept when she thought of her youth
And all of the chances
She missed at school dances
And once in a telephone booth
there was an old girl from salecia
who said if my c%nt doesn’t please ya
you may as well cum
up my slimy old bum
but be careful my tapeworm don’t seize ya
From matt_mcl:
There was a young girl of Vancouver,
Who, when told it was not ‘horses doover,’
Found she hadn’t the nerve
To ask for hors d’oeuvres,
So had soup as a saving manoeuvre.
More Asimov:
A woman from North Carolina
Stretched fiddle strings 'cross her vagina
And with proper size cocks
What was sex became Bach’s
Toccata and Fugue in D Minor.