This paper studies the prevalence and security impact of open tunnelling hosts on the Internet. These hosts accept legacy or modern tunnelling traffic from any source. We first scan the Internet for vulnerable IPv4 and IPv6 hosts, using 7 different scan methods, revealing more than 4 million vulnerable hosts which accept unauthenticated IP in IP (IPIP), Generic Routing Encapsulation (GRE), IPv4 in IPv6 (4in6), or IPv6 in IPv4 (6in4) traffic. These hosts can be abused as one-way proxies, can enable an adversary to spoof the source address of packets, or can permit access to an organization's private network. The discovered hosts also facilitate new Denial-of-service (DoS) attacks. Two new DoS attacks amplify traffic: one concentrates traffic in time, and another loops packets between vulnerable hosts, resulting in an amplification factor of at least 16 and 75, respectively. Additionally, we present an Economic Denial of Sustainability (EDoS) attack, where the outgoing bandwidth of a host is drained. Finally, we discuss countermeasures and hope our findings will motivate people to better secure tunnelling hosts.