Prioritizing rows in a union

I just remembered a pretty common data challenge the other day. Suppose you have a number of tables, all with similar information in them. You want to union their contents, but you need to prioritize them, so you want to choose all the rows from table A, then rows from table B that are not included in A, then rows from C that are not included in A or B, and so on.

This is a pretty common use case in data cleansing or data warehousing applications. There are a few different ways to go about this, some more obvious than others.