Many twin researchers occasionally encounter twin pairs displaying unusual physical, medical or behavioral traits. Unfortunately, these interesting cases are often unreported because they do not fit in easily with ongoing projects. However, these “odd cases” may suggest new hypotheses, new designs or entirely new projects. In this paper, I argue in favor of publishing case studies of exceptional twins, and refer to several large scale studies inspired by such reports. Several informative case studies are then summarized: DZ twins discordant for hyperinsulinism, DZ twins born after ICSI, “simultaneous madness in twins, and sixteenth century conjoined twins. The article concludes with a review of parenting twin pandas.