We consider the effect attackers who disrupt anonymous communications have on the security of traditional high- and low-latency anonymous communication systems, as well as on the Hydra-Onion and Cashmere systems that aim to offer reliable mixing, and Salsa, a peer-to-peer anonymous communication network. We show that denial of service (DoS) lowers anonymity as messages need to get retransmitted to be delivered, presenting more opportunities for attack. We uncover a fundamental limit on the security of mix networks, showing that they cannot tolerate a majority of nodes being malicious. Cashmere, Hydra-Onion, and Salsa security is also badly affected by DoS attackers. Our results are backed by probabilistic modeling and extensive simulations and are of direct applicability to deployed anonymity systems.