OEM Grid Control Template
Oracle implemented monitoring templates a bit differently than you might expect.  When you apply a template to a database it doesn't associate the template with the database, but instead applies the template settings to the database.  This is why modifying the template after it has been applied to the database has no effect until it is re-applied to the database.  

The 11.1 Oracle Enterprise Manager documentation explains how to use the "Compare Monitor Template" feature to determine how closely the template matches a particular target.  In this way you can determine if the template has been applied to the database.


  Deciding how and when to apply a template is simplified by using the
  Compare Monitoring Template feature. This feature allows you to see at
  a glance how metric and policy settings defined in a template differ
  from those defined on the destination target. Compare Monitoring
  Template is especially useful when working with aggregate targets such
  as groups and systems. For example, after you apply a Monitoring
  Template to a group, you want to verify that the group members now
  have the same monitoring settings as the template. The Compare
  Monitoring Template feature makes checking simple. You can also
  schedule this as a report, allowing you to check periodically if the
  group members still follow the template settings.