There are many reasons why we might want to split up groups of tables or applications: security, resource control, convenience. Whatever the reason, we often need to separate groups of tables (I avoid saying the word "database" just to avoid various confusions).
This topic is frequently referred to as multi-tenancy, though that is not a fully accepted term as yet.
The purpose of this recipe is to discuss the options and lead into other more detailed recipes.
If you want to run multiple physical databases on one server, then you have four main options, which are as follows: