My mother used to tell me that I shouldn't give our kitten cow milk, even if she seemed to enjoy it. Since I loved my kitten, and was quite disobedient at that time, I did it fairly often, and never observed any unwelcome consequences.
I did a little bit of research and found several topic-related links.
Generally speaking, no, cats shouldn't drink milk. Most cats are lactose (which refers to the sugars in milk) intolerant, and drinking milk may result in an upset tummy or cause diarrhoea.
And another quote.
Once cats mature, many become lactose intolerant. This makes cow's milk a poor choice to use as a treat for your cat. Milk can cause your pet to have stomach ailments and indigestion since they are not used to it. In some cases milk can actually make your cat very ill and cause vomiting and/or diarrhea.
However, these articles seem, scientifically speaking, poorly documented. Some of them recommend a special brand of milk designed for cats, which makes me suspect they might have commercial interests in warning people against generic cow milk.
So, what's the truth in it? Is there a solid, biological reason why cats shouldn't drink cows' milk?