here are the pets I can think of, and find that are illegal to own in California.

Gars
African clawed frog
Alligators
Caimans
Snapping turtles
White-eyes (Zosterops)
Monk (Quaker) parakeet
Short-tailed opossum
Sugar glider
Hedgehogs
Degu
All gerbils and jirds (like the Duprasi)
Dormouse (any)
Cacomistle
Coatimundi
Skunks
Arctic fox (blue fox)
Fennec fox
Wolf-dog hybrids*
Ferret
African lion
Serval
Flying squirrels
All chipmunks and squirrels
Prairie dogs
Gambian giant pouched rat
African striped grass mouse (zebra mouse)
African pygmy mouse
Egyptian spiny mouse
Raccoon
Ringtail
Monkeys, includes chimpanzees