Generally speaking, no, cats shouldn't drink milk. Once they have weaned, most cats are lactose (sugars in the milk) intolerant, as they are no longer able to produce adequate amounts of the enzyme lactase, which is necessary to properly digest milk.
In the lactose intolerant cat, when he drinks milk, because his body doesn't produce enough lactase, he is unable to break it down into simple sugars, which would then be absorbed into his bloodstream. Instead, it remains in the digestive system where bacteria cause it to ferment. It is this fermentation process that leads to the typical symptoms such as gas, bloating and diarrhea.
Young kittens MUST have milk in order to survive. The weaning process begins around four weeks of age, but prior to that their only source of nutrition is milk. It is extremely important that you do not give a young kitten cow's milk. The best possible milk is from the kitten's own mother. If the kitten is orphaned and a foster cat can't be found for the kitten, then the kitten will have to be given a specially designed kitten formula, which can be purchased from your veterinarian. This is specifically designed for kittens (cow's milk is suitable for baby cows, who have different nutritional requirements than kittens).
Are all cats lactose intolerant?
Not all cats are lactose intolerant, however, the only real way to find out if your cat is, is to try giving him some milk to see if it causes diarrhea. If you find your cat is okay with cow's milk, then the occasional bowl is fine; but this should be given as a treat only.
Cat Milk Alternatives:
If you want to give your cat milk, the safest bet is to purchase special lactose free cat milk from your supermarket or pet store.
Nutritionally, it is not necessary to give your cat milk. If they are fed a balanced diet, they receive all the nutrients they require via their food. Also, milk contains calories (water has none) that your cat is already receiving via his food. Obesity has serious health implications for cats.
Fresh water should always be available to your cat.