Targeted advertising can benefit consumers through lower prices for access to websites. Yet, if consumers dislike that websites collect their personal information, their welfare may go down. We study competition for consumers between websites that can show targeted advertisements. We find that more targeting increases competition and reduces the websites' profits, but yet in equilibrium websites choose maximum targeting as they cannot credibly commit to low targeting. A privacy protection policy can be beneficial for both consumers and websites. If consumers are heterogeneous in their concerns for privacy, a policy that allows choice between two levels of privacy will be better. Optimal privacy protection takes into account that the more intense competition on the high-targeting market segment also benefits consumers on the less competitive segment. Consumer surplus is maximized by allowing them a choice between a high targeting regime and a low targeting regime which affords more privacy.