The Internet's tremendous value is undoubtedly dependent on its universal connectivity among a great number of heterogeneous networks that are distributed over the world. In recent years, while the Internet's scale has expanded exponentially, the current status of its connectivity is still in the lack of comprehensive and formal study. In this paper, we contribute to the understanding of Internet's IP-layer connectivity by quantitatively measuring the reachability from 124 PlanetLab nodes towards 197869 diversely distributed destination IP addresses. We first demonstrate our methodology to meet the challenges in experiment design, and then statistically analyze the Internet's IP-layer connectivity in various aspects, including the directly reachable proportion, packet loss, delay variation, and the effect of domain and geographic distance. Finally, we investigate main causes of IP-layer unreachability by revealing some intentional insulation policies based on empirical study on a few special cases and analyzing its correlation to typical routing issues.