OpenSourse - Free Databases for Linux Operating System
Oracle's MySQL is one of the most popular GPL'ed databases for the GNU/Linux and BSD platforms. MySQL database is popular because of fast performance, high reliability, ease of use, and dramatic cost savings.
SQLite Embeddable SQL Database Engine is a C library that implements a self contained, serverless, zero configuration, transactional SQL database engine. This allows application programmers to embed an SQL server directly into their application. SQLite is the most widely deployed SQL database engine in the world. The source code for SQLite is in the public domain. The latest version of SQLite is 3.7.3 and it is recommended for all new development.
Mckoi SQL Database is an Open Source SQL Database System written in Java. Supports transactions, referential integrity, triggers, indexes, Java specific enhancements. Supports multi-threaded, multi-client operation; embedable. Released under the GPL license. This is probably the most advanced open-source pure Java database out there. The latest version of Mckoi SQL Database is version 1.0.3.
SAP MaxDB (formerly SAP DB) is the liberation, under the GPL/LGPL license, of the SAP AG database. This is a major enterprise class database. The latest update of SAP MaxDB is 7.7.07.16
HyperSQL is written in a Java SQL relational database engine, its core is completely multi-threaded, supporting two-way locking and MVCC (multi version concurrency control), almost complete support for ANSI-92 SQL, support for common data types, the latest version of the increase BLOB and CLOB data for the support, the maximum amount of data to support up to 64T A stable version 2.0.1 RC1 now available.
PostgreSQL is a powerful and complete SQL implementation that rivals commercial databases such as Oracle. This database (along with MySQL) is the leading GPL'ed database system for the GNU/Linux & BSD platforms. Commercial support is available from a company formed by the leading Postgres developers. The latest version of PostgreSQL 9.0 is now available.
GigaBASE and FastDB
GigaBASE and FastDB are memory & file-based databases with an SQL-like query language. Because they compile into an application, they avoid most of the DB management problems of client-server. BSD-like license.