Large language models excel at performing inference over text to extract information, summarize information, or generate additional text. These inference capabilities are implicated in a variety of ethical harms spanning surveillance, labor displacement, and IP/copyright theft. While many policy, legal, and technical mitigations have been proposed to counteract these harms, these mitigations typically require cooperation from institutions that move slower than technical advances (i.e., governments) or that have few incentives to act to counteract these harms (i.e., the corporations that create and profit from these LLMs). In this paper, we define and build "data defenses" -- a novel strategy that directly empowers data owners to block LLMs from performing inference on their data. We create data defenses by developing a method to automatically generate adversarial prompt injections that, when added to input text, significantly reduce the ability of LLMs to accurately infer personally identifying information about the subject of the input text or to use copyrighted text in inference. We examine the ethics of enabling such direct resistance to LLM inference, and argue that making data defenses that resist and subvert LLMs enables the realization of important values such as data ownership, data sovereignty, and democratic control over AI systems. We verify that our data defenses are cheap and fast to generate, work on the latest commercial and open-source LLMs, resistance to countermeasures, and are robust to several different attack settings. Finally, we consider the security implications of LLM data defenses and outline several future research directions in this area. Our code is available at https://github.com/wagnew3/LLMDataDefenses and a tool for using our defenses to protect text against LLM inference is at https://wagnew3.github.io/LLM-Data-Defenses/.