You can check the Supported Plattforms to find supported databases - you just have to eliminate the commercial databases which are only supported with Alfresco Enterprise Edition.
Specifically, Alfresco supports running on MySQL and PostgreSQL. MariaDB also works, assuming you use a JDBC driver which fully emulates MySQL (newer versions of the driver report themselves as MariaDB instead of MySQL, which breaks the support - not sure if Alfresco is planning to address that).
