Edward Lear made the form popular for children, and Anon wrote the great dirty limericks, and Garrison Keillor does both while pushing the limerick envelope. E.g.

Here is a yawp for old Walt
Whitman, who's well worth his salt
Though sometimes he'll slip
And just let her rip
And say: "Camerados! What is this blade of grass? Who am I?
Who are you?" And you have to say HALT.

Of course he deals in the vulgar. And the semi-salacious:

Chopin wrote a lovely etude
That, when performed in the nude
By a mademoiselle
Who plays fairly well
Can certainly uplift the mood.

Many are educational, including his 26-limerick abecedary for English majors. And also:

The Confederate general Bob E. Lee
Committed treason quite freely
And General Grant
Beat him up cause you can't
Attack federal troops...I mean really.
He's written limericks in honor of friends, members of the New York Philharmonic, his daughter's teachers, a quintuple for Emily Dickinson, and one for his ophthalmologist.

My eye surgeon, good Dr. Khanna,
Looked through her eyepiece down on a
Novelist's retina
Who thought he was gettin' a
Vision of the blessed Madonna.

Woven through the verses are terse reflections on daily life, work, faith, and the old man of St. Paul whose office was a toilet stall.