Law of Demand is an assertion. We need not question it if its testable implications have not yet been refuted. But quite a lot of people always challenge such a law and doubt its predictive power. On the other hand, some people use the case of luxury goods, which in my eyes it's invalid, to refute the law. They suggested that the higher the prices, the higher the quantity demanded of luxury goods, because the buyers want to show their wealth off by buying higher prices luxury goods. However, the people who suggested this idea do overlook an important point....
order to exclude other factors that may affect the price. In other words, we only want to know the response of quantity demanded on a change in the price. When the prices of luxury goods rise, their luxury level will increase too, and this violates the assumption of other things being equal. According to Law of Demand, holding other things ,including the luxury levels of luxury goods, being unchanged, when the prices of luxury goods increase, their quantity demand will decrease.

Up until now, it seems that there is no valid example that can prove Law of Demand wrong.