I've heard it said that there's no such thing as a good clean limerick. I would have to disagree; I like clean limericks. But then, most of the best clean limericks aren't really limericks at all. To be more precise, my favorite limericks are mostly the ones that play with or comment on the limerick form, directly or indirectly: meta-limericks of one kind or another.
Most ordinary limericks don't rhyme or scan nearly as well as I'd like; I figure if you're going to use a fairly strictly defined verse form (like limericks, haiku, double-dactyls, or sonnets) you ought to stick to the restrictions of that form unless you have a good reason not to (though admittedly limerick scansion is a good deal looser than that allowed for, say, double-dactyls). There are plenty of non-scanning limericks out there, especially in theatre games; I prefer the ones that either scan well or are quite aware that they don't, like this one (with no attribution I'm aware of):
There was a young bard of Japan
Whose limericks never would scan
When they said it was so,
He replied, "Yes, I know,
But I always try to fit as many syllables into the last line as I possibly can."
And taking non-scansion in the opposite direction:
There once was a fellow from Xiangling
Whose greatest delight was in mangling
Poems. He would drop
Words between lines and lop
Their ends off, and leave readers dang
Playing with the rhyme scheme rather than the scansion, a renowned Victorian versifier wrote:
Limerick in Blank Verse
There was an old man of St. Bees
Who was stung in the arm by a wasp.
When they asked, "Does it hurt?"
He replied, "No, it doesn't,
But I'm sure glad it wasn't a hornet."
—Sir William S. Gilbert
Even the number of lines is not a constant, as in this pair of anonymous items:
There was a young man from Peru
Whose limericks stopped at line two.
There was a young man from Verdun.
And then, as Elliott Moreton and Carl Muckenhoupt have been known to remark, there's the one about the Emperor Nero.
Some years back, Elliott and Carl produced The Oxford Book of Meta-Limericks (privately published, Oxford, MS, ca. 1989), now sadly out of print. The following limericks are quoted from that slim volume, by kind permission of the authors.
More limericks with pieces missing:
There was a Soviet captain named XXXXXXXXXX
Who was a XXXXXXX technician in XXXXXXXXX.
He was XXXXXXXXXXXXXXXXXX
For failure to clear
Limericks with his superiors.
A lady whose name was McCord
Once over this limerick pored
To find the evil design
Hidden in the last line—
But alas, she could not see the .
(This one is an in-joke based on the Illuminatus! trilogy.)
A cardiac patient named Fred
Made a limerick up in his head.
But before he had time
To write down the last line
Some other self-referential limericks:
There was a young poet quite fine,
Whose limericks repeated a line.
Though this was redundant,
Though this was redundant,
His limericks repeated a line.
This poem is copyright ©
By the author, 1983.
Prior written consent
Is required to present
It on radio, film, or TV.
The idea of meta-limericks can be taken a step beyond limericks that comment on themselves, to self-referential items that claim to be limericks but (by the usual definition) aren't:
Once there was a guy from Atlanta whose limericks were indistinguishable from prose.
And finally, there are items that start out disguised as limericks but turn out not to be at all. These two don't even directly claim to be limericks, but they do bring up the question of their own limerick-nature:
There once was a limerick
But this isn't it.
This isn't a limerick;
It isn't even a poem.
A newspaper poet for Hearst
Deprived of his reason
By uncontrolled sneezing
Was by phantasmal demons coerced
To write all of his limericks reversed.