Here is the next in my series of posts explaining how common tasks in DTS can now be implemented in SSIS.
Use multiple connection objects in order to maintain seperate connections to a database
It was commonly recommended in DTS that a package should contain multiple connection objects pointing to the same database if you had multiple tasks using that database. It was considered more efficient for each task to have a dedicated connection to the server.
In SSIS, DTS Connection objects have been replaced with Connection Managers. There is a good reason for the name change. A SSIS Connection Manager maintains a pool of connections to the database rather than just a single transaction therefore you only need one Connection Manager whereas in DTS you would need multiple Connection objects.
If you need to replicate the same behaviour as DTS within a SSIS package then look into using the RetainSameConnection property. There is one good use of this property as I have previously covered here.