Others I love are Roald Dahl's Dirty Beast rhymes - I learnt them all off by heart as a child and regularly recite them to my class!
I also learnt this one, having discovered it in one of my mum's old Pony Club annuals from the 60s. Used to make me giggle:
Can't remember the title but it's by John Betjeman I think:
It’s awfully bad luck on Diana,
Her ponies have swallowed their bits
She fished down their throats with a spanner
And frightened them all into fits.
So now she’s attempting to borrow.
Do lend her some bits, Mummy, do;
I’ll lend her my own for to-morrow,
But today I’ll be wanting them too.
Just look at Prunella on Guzzle,
The wizardest pony on earth
Why doesn’t she slacken his muzzle
And tighten the breech in his girth?
I say, Mummy, there’s Mrs. Geyser
And doesn’t she look pretty sick?
I bet it’s because Mona Lisa
Was hit on the hock with a brick.
Miss Blewitt says Monica threw it,
But Monica says it was Joan,
And Joan’s very thick with Miss Blewitt,
So Monica’s sulking alone.
And Margaret failed in her paces,
Her withers got tied in a noose,
So her coronets caught in the traces
And now all her fetlocks are loose.
Oh, it’s me now. I’m terribly nervous.
I wonder if Smudges will shy.
She’s practically certain to swerve as
Her Pelham is over one eye.
Oh, wasn’t it naughty of Smudges?
Oh, Mummy, I’m sick with disgust.
She threw me in front of the Judges,
And my silly old collarbone’s bust.
He also wrote a very good one about post war Britain, called Slough.