Do you play sports? What sports?

It should be either “Do you play any sports?” or “Do you play a sport?” This is the natural way to ask this kind of question, where ‘any’ functions as the plural of ‘a,’ the indefinite article, in questions and negative statements. Similarly, we’d ask either “Do you have any problems?” or “Do you have a problem?” and we might answer either “No, I don’t have any problems” or “No, I don’t have a problem.”

However, we might use ‘any sport’ to stress that it doesn’t matter which one, e.g. A: “I don’t play tennis, I hate softball, and golf nauseates me. Soccer is for children, and don’t talk to me about lacrosse.” B: “Really? Do you play any sport at all?”