Equality of opportunity with respect to health outcomes is severely understudied, while in contrast the cases of income and education have received ample attention in the economic literature. This paper is the first to analyze the importance of family background for health in a cross-country comparison. Using comparable survey data we study sibling correlations in five health outcomes in three countries with different institutions and characteristics in terms of health care provision and income inequality: Denmark, Germany and the US. The main findings are that no country comes out unequivocally as the most mobile, although, perhaps surprisingly, the US exhibit lower sibling correlations on the most outcomes. Exploring simple variance decompositions we show that higher inequality (variance) in US outcomes drives these results, underscoring how sibling correlations measure the relative importance of family background. Our findings are robust to inclusion of various parental socioeconomic controls.