1.Cats are my favorite pet.(correct) 2.The cat is my favorite pet. (probably grammaticly correct, but it sounds awkward so I would avoid using it) 3.A cat is my favorite pet. (Awkward) 4.The cats are my favorite pet. (Awkward) 5.The cats are my favorite pets. (Can really only be used if referring to a specific group of cats but in that case you'd probably be better off using "These cats are my favorite pets.") 6.Cats are my favorite pets. (Also correct but slightly changes the meaning of what you're saying compared to the first sentence.) 7.Cat is my favorite pet. (Not correct) 8.Cat is my favorite pets. (Not correct) 9.My favorite pet is cats. (Sounds a little awkward to me but also correct) 10.My favorite pet is the cat. (Correct but also a little awkward) 11.My favorite pet is a pet. (awkward) 12.My favorite pet is the cats. (Awkward) 13.My favorite pets are the cats. (Awkward) 14.My favorite pets are cats. (Correct but you're speaking completely in plurals) 15.My favorite pet is cat. (Awkward) 16.My favorite pets are cat. (Incorrect. You would have to make both nouns plural for it to make sense.) To be fair, I'm no english teacher and even the ones I labeled as awkward I'm not 100% sure they're incorrect or correct but I would try to avoid them in conversation and writing. Hopefully this is of some help to you.

It depends on what you mean. Some of these are ok. Some of them change the meaning. Some are odd sounding, but do not have problems grammatically. Some are just plain wrong. 1.Cats are my favorite pet. (This means that cats are your favorite type of pets. You like them better than birds or rabbits or dogs or whatever) 2.The cat is my favorite pet. (This means that you have 2 or more pets - but a specific cat is your favorite) 3.A cat is my favorite pet. (This sounds odd, but it isn't incorrect. Means the same as #1) 4.The cats are my favorite pet. (wrong) 5.The cats are my favorite pets. (Look at #2 - you have many pets. The cats are your favorites.) 6.Cats are my favorite pets. (This is fine and equivalent to #1) 7.Cat is my favorite pet. (wrong, unless one of your pets is named "Cat") 8.Cat is my favorite pets. (very wrong) 9.My favorite pet is cats. (This doesn't work) 10.My favorite pet is the cat. (This is correct, but sounds very strange) 11.My favorite pet is a cat. (Again, correct, but very strange unless you're about to start telling me about a very specific cat that is your favorite.) 12.My favorite pet is the cats. (wrong) 13.My favorite pets are the cats. (Also very strange, unless again, you have multiple types of pets and you only like the cats) 14.My favorite pets are cats. (correct) 15.My favorite pet is cat. (wrong) 16.My favorite pets are cat. (very wrong)