The most interesting example comes from a case in 1973 where UC Berkeley was sued for discrimination against women in graduate school admissions. The data of percent acceptance indisputably show that, if a male applies, it is more likely for him to be admitted than if a female applies (44% vs. 35%). At first glace, one may propose the causal conclusion that Berkeley is biased against females.
However, if we partition the data by department to investigate the most discriminatory department, we reveal that, in 4/6 of the departments, a female applicant is more likely to be accepted than a male applicant. In the remaining two departments, the disparity between men and women is not nearly as drastic as the amalgamated data above. This data refute the causal conclusion that Berkeley has a significant bias against women.
Several other examples, such as batting averages, kidney stone treatments, and birth weights, of a real-life Simpson's paradox can be found on the Wikipedia page  where this data were taken from.
 P. J. Bickel, E. A. Hammel, J. W. O'Connell. Sex Bias in Graduate Admissions: Data from Berkeley. Science 187, (4175). 1975. pp. 398-404.