We present a comprehensive survey of available corpora for multi-party dialogue. We survey over 300 publications related to multi-party dialogue and catalogue all available corpora in a novel taxonomy. We analyze methods of data collection for multi-party dialogue corpora and identify several lacunae in existing data collection approaches used to collect such dialogue. We present this survey, the first survey to focus exclusively on multi-party dialogue corpora, to motivate research in this area. Through our discussion of existing data collection methods, we identify desiderata and guiding principles for multi-party data collection to contribute further towards advancing this area of dialogue research.