Free databases

IBM-DB2
DB2 Express-C (Free to download, develop, deploy, distribute)

http://www-306.ibm.com/software/data/db2/udb/db2express

Oracle
Oracle Database 10g Express Edition (store up to 4GB of user data, use up to 1GB of memory, and use one CPU on the host machine)

http://www.oracle.com/technology/products/database/xe/index.html

MS-SQL
SQL Server 2005 Express Edition (free, redistributable)

http://www.microsoft.com/sql/editions/express/default.mspx

Sybase
Sybase ASE Express Edition for Linux (limited to use of one CPU, 5GB of data storage and 2GB of RAM)
http://www.sybase.com/linuxpromo

MySQL
MySQL Community Edition (GPL License)
http://www.mysql.com

PostgreSQL
All version (BSD License)

http://www.postgresql.org