Oracle 10g Express Edition

DB2 Express-C

SQL Server Express

PostgreSQL

MySQL

Stacks

Another option is to install a web infrastructure stack which includes Apache, PHP and PosgreSQL or MySQL. These exist for Windows, Mac or Linux. You can get stacks with PosgreSQL here or with MySQL here

How to interact with the databases?

The commercial databases will come with a software to connect directly to the database and write SQL queries. The open source databases (PosgresSQL and MySQL) do not. You either have to interact through the console or a third app. I recommend Aqua Data Studio. You can get an evaluation license and renew it after 14 days. I have been renewing it for several months and it still works! This app works as an interface for all databases.