Participants in human-human conversation often entrain to one another, adopting the vocabulary and other behaviors of their partners. Evidence of this has been found from laboratory studies and observations of real life situations. We are investigating many types of entrainment in two large corpora of human-human conversations to improve system behavior in Spoken Dialogue Systems (SDS). We want to discover which types of entrainment occur generally across speakers and which seem to be speaker-specific, which types of entrainment can be reliably linked to task success and perceived naturalness, and which types of entrainment can be automatically modeled in SDS. Our research has importance for the construction of better SDS. Currently, research SDS have attempted to entrain users to system vocabularies to improve speech recognition accuracy: Since users are likely to employ the same vocabulary in their answers that systems use in their queries, systems have a better chance of recognizing user input correctly if they can predict word usage. However, there has been little attempt to create SDS that entrain to user behavior, despite evidence that human beings rate humans and systems that behave more like them more highly than those that do not. Our work focuses on determining which types of system entrainment to users will be most important to users and most feasible for SDS. Our results will be disseminated through papers and presentations at speech and language conferences. We will also provide publicly available annotated corpora for future research by others.