Oracle has recently made available their Oracle Database 10g Express Edition. Its limitations are that it can only run servers with one processor, with 4GB of disk space and 1GB of memory. It is not sufficient for even a small data warehousing project, but it is great for teaching a class. It is available for Linux and Windows.
Microsoft recently made available for free its SQL Server 2005 Express Edition. Obviously only available under Windows. It lacks enterprise features, it is limited to one CPU, 1GB of memory and 4GB of disk space: basically the same limitations as the Oracle Database 10g Express Edition.
IBM is thinking about doing the same with DB2. Currently, it offers the free Java-based Cloudscape database running on any standard Java Virtual Machine (JVM). They also offer a free PHP-bound version of DB2 called Zend Core available for Linux and AIX, and to be available for Windows.
However, it is not like you are limited to what IBM, Oracle and Microsoft have to offer or have to accept the limitations of their “free” products. There are many good free and open source databases such as MySQL, PostgreSQL, MaxDB, Firebird or Ingres. None of these free alternatives is as powerful as an Oracle database, but if you compare what you can buy with zero dollars, the big guys don’t necessarily come on top.