We study the formation of networks in environments where agents derive benefits from their neighbours (immediate links) but suffer losses through contagion when any agent on a path that connects them is hit by a shock. We first consider networks with undirected links (e.g. epidemics, underground resistance organizations, trade networks). We find that the only networks that satisfy strong notions of stability are comprised of disjoint subgraphs that are complete. Then, we consider networks with directed links and we find that stable networks can be asymmetric, connected but not completely connected, thus capturing the main features of production and financial networks. We also identify a trade-off between efficiency and stability.