The question in the title needs to be clarified because I believe that the questioner is asking whether it is aright if her cat eats a bit of cereal after she has eaten it. The question is not intended to ask whether it is alright to feed your cat cereal all the time. Perhaps that goes without saying but it needs to be clarified, I believe. Note: the question is asked on Google.
So the question could be reformulated, “is it all right if my cat eats a bit of cereal from time to time?”
And the answer to this is yes, it is alright in my opinion. However there are some caveats. Cereals can contain raisins and raisins are probably not good for cats and have been found to be toxic in dogs. Sometimes cereal can contain chocolate and most people by now know that chocolate and coffee can be toxic to cats due to the stimulus they contain, caffeine and theobromine.
Putting those toxic elements within cereal aside because they are not always found in breakfast cereal, cereals are made of corn, wheat or rice as far as I know. These foods are not on the list of foods which are dangerous for domestic cats.
Also, people almost invariably add milk to breakfast cereal. Milk contains fat and cats like fat. Cats will lick milk off the cereal bowl that is left over. At this quantity it is alright but most domestic cats are lactose intolerant, which means that they are unable to digest lactose, a type of sugar mainly found in milk and dairy products.
Therefore, domestic cat should not be given cow’s milk for humans on a daily basis as a drink (some cats are more lactose intolerant than others). But, as mentioned, to lick around the bowl to taste the fat in milk and perhaps to enjoy the taste of cereal, is almost certainly okay for nearly all domestic cats.
My cat likes to eat a tiny bit of cereal, the bit that I’ve left, which is very little I have to say. For him, I suspect that it is simply the taste of the milk which he likes. Incidentally, I use lactose-free milk and therefore that particular issue has been ticked off!
Associated: is it okay for cats to eat broken egg shells?