Violation of PRIMARY KEY constraint 'PK_PrimaryKeyName'. Cannot insert duplicate key in object 'dbo.TableName'.
Even when attempting to insert data directly into the table via SQL Management Studio, the same error would occur. The source of the issue was that the identity seed values were out of sync with the actual values in the table (a result of doing inserts with IDENTITY_INSERT ON). The simple fix was to change to output text mode in SQL management studio and run the T-SQL query:
SELECT 'DBCC CHECKIDENT (' + Table_Name + ')' FROM information_schema.tables WHERE TABLE_TYPE = 'BASE TABLE'
Run the output of this query - this corrected all the 'duplicate key' issues I was having after the deploy of the database scripts.