There are many reasons why we might want to split groups of tables or applications: security, resource control, convenience, and so on. Whatever the reason, we often need to separate groups of tables (I avoid saying the word database, just to avoid various kinds of confusion).
This topic is frequently referred to as multitenancy, though it is not a fully accepted term as of yet.
The purpose of this recipe is to discuss the options and lead to other, more detailed recipes.