It's practically a cliche in cartoons, books and movies - a cat happily living on endless pints of milk and cream, and lots of fish.
The truth, however, is more complex.
Cats & milk
Surprisingly, many cats are lactose-intolerant. Drinking milk (especially cow's milk) gives them diarrhoea, which may lead to dehydration. Other cats which are not lactose-intolerant enjoy milk and can drink some occasionally without ill-effect. However, milk does not contribute to a cat's nutritional needs, so it is not necessary for a cat to drink it as part of its diet!
The only time a cat truly needs milk is when it is a kitten, drinking its mother's milk - in other words, it needs only cat's milk when it is young, not cow's or goat's milk. Kittens have an enzyme, lactase, that allows them to digest their mother's milk. As they grow up, many cats lose the enzyme. A young adult cat that can initially handle cow's milk may develop intolerance to it as the levels of the enzyme fall. Thus, a cat that used to be able to drink milk without a digestive upset may not always be able to do so.
If your cat loves milk, but is lactose-intolerant, consider buying a milk substitute from your pet store that is formulated just for cats.
Cats &fish
Some fish is good for cats, as it is for humans. But it is not a "complete" feline food, so it can become a bad thing if it is the only thing you feed your cat! Too much fish can even destroy B vitamins such as thiamine in cats, something which may result in seizures and loss of appetite.
Because feral cats hunt, scavenge and consume a wide range of foods, they have a better chance of fulfilling their nutritional needs through all the different things they eat. But pet cats are more likely to fall victim to health problems caused by a dietary imbalance - even fish supplements can throw a cat's system off-kilter. Therefore, either keep to a good-quality commercial cat food and feed according to instructions, or discuss with your vet what you must know in order to feed your cat home-prepared meals.
Watch out for the bones in fish too. Vets have seen cases of cats in pain from fish bones stuck in the throat or digestive tract.