Not jokes, but fishy favorites of mine (from Mother Goose):

A man in the wilderness,
He asked me:
"How many strawberries grow in the sea?"
I answered him,
(as I thought good):
"As many red herrings as swim through the wood!"

(A counting out rhyme [a la the Calvin and Hobbes cartoon, mentioned above):

1, 2, 3, 4, 5,
Once, I caught a fish alive.
6, 7, 8, 9. 10
Then I let it go again.
Why did you let it go?
Because it bit my finger so.
Which finger did it bite?
The little finger, on the right.