SQLite

SQLite is a small, fast, self-contained, full-featured SQL database engine that runs in-process rather than as a server, storing an entire database in a single cross-platform file, released into the public domain and described as the most widely deployed database engine in the world.

Having no server is the property everything else follows from, and it makes SQLite a different kind of thing from every other entry in this category. There is nothing to install, configure, start, secure or administer: an application links the library and opens a file, which is why it ships inside browsers, phones, aircraft and effectively every application that needs structured local storage.

Being in the public domain rather than merely open source removes even the licence obligation, and the practical consequence is that a company embedding SQLite in a commercial product has no attribution requirement, no copyleft exposure and no vendor to notify, which is why it appears in devices whose manufacturers would never accept a licence.

SQLite publishes an unusually direct page on when not to use it, and it is worth reading before choosing: it is a replacement for fopen rather than for a client-server database, so high write concurrency and multiple machines sharing one database are the cases it explicitly does not serve. The test suite is famously exhaustive. SQLite is free.