Bottom line: no, not cow's milk. The image of "cats and their bowl of milk" is a myth invented by cartoons.
As kittens, cats have the enzyme (lactase) that breaks down the lactose in their mother's milk, but once they're weaned, that enzyme drops off sharply in adult cats. So when they drink cow's milk, they can't digest the lactose, and diarrhea, vomiting, and stomach pain easily follow. It's the same situation as a lactose-intolerant person gulping down a glass of milk.
Many owners try to use milk to keep their cat hydrated, but the right answer is water and wet food. Even cat-specific milk has calories, so giving too much leads to weight gain. Start by checking whether your cat is drinking enough water with the water intake calculator, and if it's falling short, the real fix is approaches like adding a water fountain or combining in wet food.
A small lick is usually fine. Watch for diarrhea or vomiting over the next half day to a day, and if the symptoms persist, or if your cat is very young or elderly, contact your vet. It can become dangerous if dehydration sets in as well.
Fermentation lowers the lactose, so they're better than milk, but they're high in fat and salt, so they aren't a recommended treat. If you do offer some, give unsweetened plain yogurt in a small amount (less than a teaspoon) and watch how your cat reacts.
The ability to break down lactose varies from cat to cat, so some cats are fine. That said, even when there's no obvious problem, milk offers no nutritional benefit and only adds calories, so the general recommendation is that there's no real reason to give it.
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This content is general information and does not replace veterinary diagnosis. If your pet shows unusual symptoms after feeding, contact a vet.