Multi-homed and overlay networks are two widely studied approaches aimed at leveraging the inherent redundancy of the Internet's underlying routing infrastructure to enhance end-to-end application performance and availability. However, the effectiveness of these approaches depends on the natural diversity of redundant paths between two endhosts in terms of physical links, routing infrastructure, administrative control and geographical distribution. This paper quantitatively analyzes the impact of path diversity on multi-homed and overlay networks and highlights several inherent limitations of these architectures in exploiting the full potential redundancy of the Internet. We based our analysis on traceroutes and routing table data collected from several vantage points in the Internet including: looking glasses at ten major Internet Service Providers (ISPs), RouteViews servers from twenty ISPs, and more than fifty PlanetLab nodes globally distributed across the Internet. Our study motivates new research directions-constructing topology-aware multi-homing and overlay networks for better availability.