1) Veblen Effect: The law of demand does not hold on goods that have a snob appeal or prestige value. Economist Veblen calls this as conspicuous consumption. Certain goods are demanded by rich people because of their social prestige.
2) Speculative Effect: It applies in stock market when people buy maximum stocks when the price is the lowest. Although it's a short term phenomenon.
3) Giffen Goods or Giffen paradox: He poor people will buy more of inferior goods if there price rises and demand less if the price rises. In the 19 th century, in Ireland, Giffen observed that a major part of their income was spent on potatoes ( inferior good). When the price of potato increased they reduced the purchase of meat to continue buying the same amount of potato.
4) Scarcity, inflation, price delusion... etc: Expectation of price to increase in the future, buyers will buy more at higher price .