Increased global integration of firm, production, and financial networks has the potential to benefit growth but also amplify the transmission of crises. We test whether higher global connectedness is associated with robust (beneficial) or fragile (harmful) behavior using networks derived from firm equity returns across all industries (1991-2016). More globally connected firms are less likely to be in distress, with higher profit, revenue, and equity price growth; however, they are more exposed to direct contagion from distressed neighboring firms. Our analysis reveals the centrality of finance, increased globalization, and greater potential for crises to spread globally when they do occur.