When astronomers showed Earth was lowly,
not Heaven's sweet center most holy,
Philosophers grumbled
at theories crumbled.
As one said, “I wish someone had Ptolemy.”

As the poets have mournfully sung,
death takes the innocent young,
the rolling in money,
the screamingly funny,
and those who are very well hung.
(by W.H. Auden)

There was a young lady from Nachez
whose clothing was always in patches.
When she was asked why,
she replied, with a sigh,
“Because, when Ah itches, Ah scratches.”

For this limerick, you have to know that the English town Salisbury is also called Sarem, and that's how many people pronounce “Salisbury.” “Hants” is a familiar (to Brits) abbreviation of Hampshire:

There was a young vicar from Salisbury
whose manners were quite halisbury-scalisbury.
He went around Hampshire
without any pampshire
'til his bishop compelled him to walisbury.

For the following limerick, be aware that “spring” can mean a season of the year, a source of water, and a leap. “Fall” can mean a season of the year, a source of water, and tripping and falling down. This is the only triple-pun limerick I know:

There was a young fellow named Hall
who died in the spring in the fall.
'Twould have been a bad thing
had he died in the spring
but he didn't — he died in the fall.

The last word of this one is a pun. . . .

The youths who frequent picture palaces
have no need for psychoanalysis.
And though Dr. Freud
is distinctly annoyed
they cling to their long-standing fallacies.

There was an enchanting young bride
Who ate many green apples and died.
The apples fermented
inside the lamented
and made cider inside her inside.

There was a young girl from Rabat
Who had triplets: Nan, Pat, and Tat.
It was fun in the breeding,
but hell in the feeding,
as she found she had no tit for Tat.

A swimmer whose clothing got strewed
by breezes that left her quite nude
saw a man come along,
and unless we are wrong,
you expected this line to be lewd.

There once was a girl named Irene
who lived on distilled kerosene.
But she started absorbin'
a new hydrocarbon
and since then has never benzene.

A crafty young bard named McMahon,
whose poetry never would scan,
once said, with a pause,
“It's probably because
I'm always trying to cram as many extra syllables
        into the last line as I possibly can.”

Miss Farad was pretty and sensual
and charged to a reckless potential.
But a rascal named Ohm
conducted her home.
Her decline was, alas, exponential.

“Ten times now, dear Daphnis,” said Chloë,
“you have told me my bosom is snowy.
You have made a fine verse on
Each part of my person.
Now DO something — there's a good boy.”

“Yap” is a real place, a small group of islands in the west Pacific.

There was a young lady from Yap
who had acne all over her map.
But in her interstices
Lurked a far worse disease
Commonly known as the clap.

There was a young plumber named Lee
who lay plumbing his girl by the sea.
She said, “Oh! Stop plumbing!
There's somebody coming!”
Said the plumber, still plumbing, “It's me.”

There was a young vampire named Mable
whose periods always were stable.
So every full moon
she took out a spoon
and drank herself under the table.

A rabbi from far-off Peru
was desperately trying to screw.
His wife said, “Oy vey!
If you keep on this way
the Messiah will come before you.”

There once was a mathematician
Who preferred an exotic position.
'Twas the joy of his life
to achieve with his wife
topologically complex coition.

There was a young fellow named Clyde
who fell in an outhouse and died.
Along came his brother
and fell in another
and now they're interred side by side.

Archimedes, that well-known truth-seeker,
jumped out of his bath with “Eureka!”
He ran half a mile
wearing only a smile
and became the very first streaker.

A Christian Scientist from Theale
said “I know that my pain is not real.
When I sit on a pin
and it punctures my skin
I dislike what I fancy I feel.”

While Titian was mixing rose madder
His model ascended a ladder.
Her position to Titian
Suggested coition
So he climbed up the ladder and had her.

There once was a nympho named Jill
who tried dynamite for a thrill.
They found her vagina
in North Carolina
and bits of her tits in Brazil.

There once was a duchess from Bruges
whose c—t was amazingly huge.
Said the king to this dame
as he thunderously came,
“Mon Dieu! Apres moi, le deluge!”

There once was a man from Racine
who invented a f—ing machine.
Concave or convex,
it could serve either sex,
but oh, what a bother to clean!

A double limerick:

Said Einstein, “I have an equation
that some may think Rabelaisian.
Let V be virginity
approaching infinity
and P equal constant persuasion.

Now, let V over P be inverted
and the root of persuasion inserted
It is easy to see
the result, Q.E.D.
is a relative,” Einstein asserted.

A triple limerick (pretty vulgar):

There were two young ladies from Birmingham.
Shall I tell you the story concerning 'em?
They lifted the frock
and diddled the cock
of the bishop as he was confirming 'em.

Now the bishop was nobody's fool.
He had been to a large public school.
So he dropped down his britches
and diddled those bitches
with his six-inch episcopal tool.

Said one girl as the bishop withdrew,
“Not bad for a bishop, 'tis true.
But the prick of the vicar
is thicker and quicker
and three inches longer than you!”

This is the only one that's really filthy, but it IS a classic.

There was a young man from Nantucket
whose <bleep> was so long he could <bleep> it.
He said with a grin
as he wiped off his chin,
“If my ear were a <bleep>, I could <bleep> it.”