GeoNames: Open source database of over 10 million names available for download free of charge under a creative commons attribution license.
Getty Thesaurus of Geographic Names Online: Worldwide coverage of place names, the Getty vocabularies are structured and available as linked open data. Emphasis is on places related to the Getty's collections in art and architecture.
Geographic Names Information System (GNIS): Database of places in the US and its territories as sanctioned by the United States Board on Geographic Names
U.S. Census Bureau Gazetteer Files: Census produced files of US places since 1990.
Nominatim is an open source gazetteer built from Open Street Map data. Source data for several free (and not-free) geocoding services.
OpenAddresses is an open source database of street addresses worldwide.