A simple classic:
There was a young man from Nantucket
Who kept all his cash in a bucket
But his girlfriend called Nan
Ran off with a man
And as for the bucket, Nan took it.
A mosquito cried out in pain:
“A chemist has poisoned my brain!”
The cause of his sorrow
was para-dichloro-
diphenyl-trichloroethane.
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There was a young lady from Ealing
Who had a peculiar feeling
So she laid on her back
Diddled her crack
And squirted all over the ceiling
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The jolly old bishop of Birmingham,
He buggered two maids while confirming 'em.
While they knelt before God,
He excited his rod,
And pumped his episcopal sperm in 'em.
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To keep a vague topicality:
A football supporter in blue
Gave his favourite sister a screw.
He said with aplomb:
“You’re better than Mom.”
Said she: “That’s what Dad told me too.”
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Spotted before, but then so is mine in its pre-amended version…
Apologies for duplication but not for resurrection. That thread was a bit before my time.
Nothing to apologise for, I just have a memory for these things…
Give it time mate… 
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And another in the same vein, from a different era:
There once was a monarch named Ed
Who screwed Mrs. Simpson in bed.
As they bounced up and down,
He yelled, “Bugger the Crown!
We’ll give it to Bertie, instead!”
One last offering
From the depths of the crypts at St. Giles
Came a shriek that resounded for miles.
Said the vicar, “Good gracious!
Has Father Ignatius
Forgotten the Bishop has piles?”
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There was a young man from Darjeeling
Who boarded a bus bound for Eling.
It said on the door
“Please don’t spit on the floor”
So he stood up and spat on the ceiling.
This is my favourite - very erudite and helped me to remember the value through my working life!
Tis a favourite project of mine
A new value of Pi to assign.
I would fix it at 3
Cause it’s easier you see
Than 3 point 14159
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In a similar vein:
A dozen, a gross and a score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Is nine squared and not a bit more.
It is you know…
It’s right if you put in the right brackets.
There once was an MP called Owen
Whose income was steadily growing
'Til they found out one day
The source of his pay
Now the cash will stop flowing: he’s going! 
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The first beer made me post here by mistake
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I was going to say…