J.A. Cuddon’s highly idiosyncratic Dictionary of Literary Terms & Literary Theory, which is highly recommended and much more fun than it sounds, gives an entirely inappropriate three pages to limericks (you can see Cuddon having one heck of a lot of fun with that). My favorite, stolen from there:
Titian was mixing rose madder.
His model posed nude on a ladder.
Her position to Titian
Suggested coition.
So he nipped up the ladder 'ad 'er.
I likes my limericks clean. 
No offense, but I think they’re more clever that way.
There was a young lady named Kite
Whose speed was much faster than light.
She left home one day
In a relative way
And returned on the previous night.
And I now see that **Seige ** posted something that’s almost identical. Oh, well.
This one depends on the vagaries of English spelling:
A young fellow named Cholmondeley Colquhoun
Once kept as a pet a babolquhoun
His mother said “Cholmondeley
Do you think it’s quite colmondeley
To feed your babolquhoun with a spolquhoun?”
Limericking an old favorite four-liner toast:
To Boston! We give it the nod
As hub of the universe; cod
And beans it is home for;
Where Lowells are known for
Conversing entirely with God.
This reminds me of my favorite limerick:
A decrepit old gas man, named Peter,
While hunting around for the meter
Struck a leak with his light,
And arose out of sight -
And as you can see by reading this, he also quite destroyed the meter.
There once was a fellow named Sweeney
Whose girl was a horrible meanie
The hatch of her snatch
Had a catch that would latch
She could only be screwed by Houdini!
From deep 'neath the crypt at St. Giles
Came a shriek that re-echoed for miles
The vicar said, "Gracious!
"It’s Brother Ignatius!
“He’s forgotten the bishop has piles!”
There once was a choirboy of Devon
Who was bugged in a haystack by seven
High Anglican priests
The lascivious beasts!
For of such is the Kingdom of Heaven
I’d hate to be kissed by a Manatee
The prospect’s too much for my vanity
Her bristly mustache
Would give me a rash
And destroy my last vestige of sanity
I’ll bet you’re the kind of guy who visits Jerusalem and doesn’t want to see the Sexiteria.
Ganked from the site mentioned in the OP:
There once was a [person] from [place]
Whose [body part] was [special case].
When [event] would occur,
It would cause [him or her]
To violate [law of time/space].
I’ve lost the first two lines of this one, I’m afraid:
[missing line 1]
[missing line 2]
I’ve never found lipstick
Adorning your dipstick,
But that’s sure FDS on your breath!
There once was a man named Bruno
Who said about sex, I do know
While women are fine,
Sheep are divine,
But Llamas are Numero Uno
That one is still my favorite…
Another good one:
There once was a girl named Melanie
Who was asked by a man “Do you sell any?”
She said, “No, sir-ee”
“I give it for free”
“To sell it, dear sir, would be a felony”
Don’t know where this came from:
There once was a man from Purdue
Whose limericks ended on line two.
And of course:
There was a sweet lass from Verdun
I’m a member of the MMOG There. I’ve been playing it since the beta started in 2003. In mid-2005, I managed to reach a skillup milestone for my avatar before anyone else. Rather than outright announce it and brag, I posted a less-than-stellar rambling poem about it, that no one “got”. When no one figured it out, aside from polite “nice poem” comments, I got more to the point with limericks, which I think worked much better:
Shall I deliver a clue-by-four beaning?
Knowledge can keep you from keening.
I give word to the wise,
Leading up to a prize!
Look deeper for a poem’s hidden meaning.
It didn’t take long for three people to rapidly get it then.
'Highfive to Oli, Peter_B, and BobbyMac!
Each wins a prize that they lack.
Acrostics are fun;
Riddles are done.
The next limerick will have a wisecrack.
('highfive and 'heart are emotes in There)
…and then for those who still didn’t get it:
There once was a member of There,
“Hallelujah!” she did declare.
“Everyone spend a while
Reviewing my profile
Except spammers who can kiss my derriere.”
My profile is set to be hidden from the idjits in that world, which IMO mostly are the spammers.
The original poem, which wasn’t a limerick, acrostically spelled out ALL LEGENDARY, which meant I’d gotten “legendary” in all the available skills… to date a feat duplicated by only one other member. I need help.
*** Ponder
One about my home town, Paw Paw, MI. My grandmother wrote this one for a radio contest many years ago and won.
There once was a lady from Paw Paw,
Who had a black crow that could Caw-Caw.
She opened the door
and watched the bird soar.
Thats the last of the bird that she saw, saw.
Stolen from that site.
There once was a man named Bertold
Who drank beer when the weather grew cold
As he reached for his cup…
“NEEEEVER GONNA GIVE YOU UP!!!”
Oh, snap! You just got limerickrolled!
Here’s a thread on Royals Review containing limericks about expectations for the Kansas City Royals 2008 season.
I recall reading this one in Reader’s Digest:
A limerick packs laughs anatomical
In a package that’s quite economical
But the good ones I’ve seen
So seldom are clean
And the clean ones so seldom are comical
One of my favorites was from an Isaac Asimov Black Widowers story, which I wish I could find in print. The gist of it is one of the characters making the point that the written form of a poem (as opposed to merely the sound) could be an essential element in its appeal, and did so by rhyming “Ms.” with “Ls.” (the latter referring to Queen Elizabeth II).
That’s fucking fantastic!!
Never gonna give, never gonna give!!
Bloody brilliant.
A young lady, born in Calcutta
One day was heard to mutter
It’s so bloody hot
The sweat from my twot
Is forming large pools in the gutter
There once were two cats from Kilkenny;
Each thought there was one cat to many.
So the fought and they fit
And they scratched and they bit
'Til instead of two cats, there weren’t any!
A flea and a fly in a flue
Were caught, so what could they do?
Said the flea, “Let us fly!”
“Let us flee!” said the fly.
So they flew through a flaw in the flue.