We study markets for sensitive personal information. An agent wants to communicate with another party but any revealed information can be intercepted and sold to a third party whose reaction harms the agent. The market for information induces an adverse sorting effect, allocating the information to those types of third parties who harm the agent most. In equilibrium, this limits information transmission by the agent, but never fully deters it. We also consider agents who naively provide information to the market. Their presence renders traded information more valuable and, thus, harms sophisticated agents by increasing the third party's demand for information. Half-baked regulatory interventions may hurt naive agents without helping sophisticated agents. Comparing monopoly and oligopoly markets, we find that oligopoly is often better for the agent: it requires a higher value of traded information and therefore has to grant the agent more privacy.