Jensen, R. T., and Miller, N. H., 2008. Giffen Behavior and Subsistence Consumption. American Economic Review 98, 1553-1577.

Abstract:

This paper provides the first real-world evidence of Giffen behavior, i.e., upward sloping demand. Subsidizing the prices of dietary staples for extremely poor households in two provinces of China, we find strong evidence of Giffen behavior for rice in Hunan, and weaker evidence for wheat in Gansu. The data provide new insight into the consumption behavior of the poor, who act as though maximizing utility subject to subsistence concerns. We find that their elasticity of demand depends significantly, and nonlinearly, on the severity of their poverty. Understanding this heterogeneity is important for the effective design of welfare programs for the poor.

A more prosaic example is the stock market.  You should also look at the classic book by Andre Gabor (1977 I think) called simply "Pricing."

You may refre to:

Giffen Behavior for Rice Consumption in Rural Bangladesh

http://www2.southeastern.edu/orgs/ijae/index_files/IJAE%20MARCH%202014%20GIFFEN%20BEHAVIOR%203-30-2014.pdf

Attached are 2 articles: one example from Japan and another Irish potato famine case. Cheers.

If I remember it correctly there is a good example of Giffen goods in Banerjee and Duflo's book "Poor Economics" (http://pooreconomics.com/about-book). The example is somewhere in the early chapters.

http://www.sfu.ca/~wainwrig/Econ400/Barzel-Suen92-giffen-demand.pdf

There are however some exceptions (to downward sloping demand). For instance, as Sir R. Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources of the poorer laboring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive farinaceous foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it.

if expenditure distribution is unimodal and the degree in which the good fails to be normal is related appropriately to the distribution then the average income effect term is negative. Thus this is the case where at least a necessary condition for Giffen effect is satisfied

Anna Rapoport (2002), Theoretical and Empirical Issues in Demand Analysis, M.Sc. Thesis, Weizmann Institute of Science, Rehovot, Israel, October 200

Giffen behavior is a phenomenon that arises entirely within the neoclassical framework where consumers care about price only inasmuch as it affects their budget sets. If demand is Giffen the good in question must also be inferior, which rules out Veblen, snob, and signaling effects.

Article Giffen Behavior and Subsistence Consumption

https://core.ac.uk/download/pdf/213990555.pdf