I’ve tagged most of the limericks by one or more subjects, and you can scroll through them by clicking the links below. 

arts and letters
bees
cats and dogs
fashion
flowers
food and drink
music
math and science
not for small children
other animals
other poetry (villanelles, epodes, etc)
politics
religion
romantic entanglements
Spelling Bee-related
word play
Nana
Simians
Sonnets