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Not all goods are treated equal by consumers, some goods are valued in good times while others are completely useless in bad times. These are exceptions to the law of demand as we have defined it.

Giffen goods
Giffen goods are named after the nineteenth century economist Sir Robert Giffen, who observed that at the time, people in Ireland bought more potatoes as the price increased. A Giffen good is an inferior good for which a rise in its price makes people buy even more of the product as a consequence of the substitution effect and the income effect for that good.

So potatoes were an example of an inferior good, meaning that demand falls as real income rises,  the income effect of a price change was so great it overcame the substitution effect.

When the price of a Giffen good rises, the substitution effect will of course reduce the quantity demanded as consumers switch away from it and over to normal goods like meat (in case of the Irish example).

Ostentatious consumption / Veblen goods
Some goods are luxurious items where satisfaction comes from knowing the price of the good. A higher price may be a reflection of quality and people on high incomes are prepared to pay for the "snob value effect". Examples would include perfumes, designer clothes, fast cars and some brand name watches. Such goods are called Veblen goods after the American economist Thorstein Veblen.

Income effect
In short; when there is a rise in the overall welfare, consumption increases.

Substitution effect
The shift in consumption at any given level of welfare, making the economy consume less of good A and more of good B.