Understanding social interaction within groups is key to analyzing online communities. Most current work focuses on structural properties: who talks to whom, and how such interactions form larger network structures. The interactions themselves, however, generally take place in the form of natural language --- either spoken or written --- and one could reasonably suppose that signals manifested in language might also provide information about roles, status, and other aspects of the group's dynamics. To date, however, finding such domain-independent language-based signals has been a challenge. Here, we show that in group discussions power differentials between participants are subtly revealed by how much one individual immediately echoes the linguistic style of the person they are responding to. Starting from this observation, we propose an analysis framework based on linguistic coordination that can be used to shed light on power relationships and that works consistently across multiple types of power --- including a more "static" form of power based on status differences, and a more "situational" form of power in which one individual experiences a type of dependence on another. Using this framework, we study how conversational behavior can reveal power relationships in two very different settings: discussions among Wikipedians and arguments before the U.S. Supreme Court.