When Apex Trigger are not Executed.

1. Cascade Delete Operations.

2. Cascade Update of Child records and reparenting as a result of Merge operation.

3. Mass Address update,Mass email Actions

4. Modifying Custom Fields data types

5. Removing or Replacing Picklist.

Best Practices with Triggers

1. Always Write Trigger in Bulkified Mode.

2. Try to Write And Use Trigger Handler Class/Code Refactoring

3. Avoid infinite Recursion.