From Muppet Wiki

Over the years Oscar the Grouch has had many pets. His diverse menagerie various dogs, a cat, a pig, several elephants, and a donkey. His favorite pet is his worm, Slimey.

Betsy Dog	Cranky Rottendoodle	Daisy Skunk	Fluffy Elephant
Iago Donkey	Preposterous Puppy	Slimey Worm	Spot Pig
Tiny Tim Cat	Various other elephants; Learning About Letters names Sophie, Blitzen, and Schopenhauer	Lassie goat (Episode 3067)

Notes

• In Episode 0793, Grover offers to become Oscar's pet, however it doesn't work out.
• In the Elmo's World installment on Farms, Oscar reveals that he has an entire farm in his trash can.
• Similar to a pet, Oscar builds Charles the Robot to follow his every command.