A variety of gazetteer resources (including Digital Chart of the World databases) in GIS formats are available through Geodata@Columbia
National Geospatial Agency (NGA) GEOnet Name Server (GNS): the official repository of standard spellings of all foreign geographic names, sanctioned by the United States Board on Geographic Names (US BGN). The database includes variant spellings, information about location, administrative division, and quality.
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.
Who's on First is an openly licensed gazatteer of over 26 million records available in a variety of formats. Source data available on their Github Repo
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.
The World Historical Gazetteer provides a collection of content and services that permit world historians, their students, and the general public to do spatial and temporal reasoning and visualization in a data rich environment at global and trans-regional scales.