Each database management system (DBMS) has different rules for using multiple geodatabases. In general, though, it is possible to create separate databases, store a geodatabase in each one, and connect to each one using separate ArcSDE services no matter what DBMS you are using.
Beginning with ArcGIS 9.2, you can also create multiple geodatabases inside one Oracle database. This model for storing multiple geodatabases in one Oracle database is in Using multiple geodatabases in Oracle as is information on creating more than one geodatabase in different Oracle databases. This is followed by topics containing specific information for storing multiple geodatabases using other DBMS types and models.
The following table lists sections of each of the DBMS-specific topics. Use it to help you find the information you need.