Some of the most commonly used free databases include:

Microsoft SQL Server Express Edition only runs on Windows-based PCs, and user database size is limited to 10 GB. This is radically smaller than the paid versions of SQL Server, at 524 petabytes.

MySQL is the popular open source database that is now owned by Oracle. It can run on Linux, Unix, Mac and Windows operating systems. Paid commercial versions with additional support are also available.

Oracle Database Express Edition runs on Windows and Linux operating systems, but the database size is limited.  It can be downloaded from here.

Oracle SQL Developer is a free integrated development that makes it easier to administer both paid and free versions of Oracle databases.