Bad smelling breath (also known as Halitosis) is not normal in cats and is usually an indication of a problem.
Most bad smells come from the mouth, more specifically the teeth. Cats get bacterial plaque on their teeth just as we do, and if this is allowed to build up, tartar is laid down. This is a hard deposit made from the calcium in saliva that adheres to the plaque and contains the bacteria. It is these bacteria that create the smell. They also produce toxins that inflame the gum and can cause erosion of the tooth roots.
The solution to this is to remove the tartar. You vet will be able to do this, but since this requires a general anaesthetic, prevention is much better than cure. The natural method for a cat to keep its teeth clean is crunching through its prey. The foods we provide for them do not have enough substance to provide for this. Feeding dry foods is better than canned for the teeth, and there are now diets which are designed to help teeth clean.
It is also possible to brush a cats teeth with a special pet toothpaste Human toothpaste is not appropriate as it is not intended to be swallowed. This is not well tolerated by many cats, even if started young. Some pet toothpaste will get some benefit without brushing, and this is often the best option in a cat.
Not all bad breath comes from the mouth. Gas produced in the colon is well known for creating smells of another kind, but what is not commonly known is that most of those same gasses are absorbed into the blood stream and are expelled by the lungs, it is only the excess which becomes flatulence. If this gas is pungent, it can cause bad breath. This is not common in cats.
This pet health article is for reference only.
If your pet is showing any symptoms or distress, and you suspect your pet is ill CONTACT YOUR VET IMMEDIATELY.