"My Collection" is cluttered with duplicates

If you delete them you won't have any data in BC. As you don't say what you use BC for its difficult to explain why you're getting lots of duplicates, but bear in mind BC uses a database that won't accept a data item having the same name, so if you keep adding the same waypoint you will end up with numerous copies of that waypoint, normally BC will simply add 1, 2, 3 etc after the waypoint name.

Perhaps you could explain more about what you're trying to do and where you think it's going wrong?

Perhaps I'm using BC wrongly. I use BC to plan trips in camper (caravan). My home address is listed at least 12 times (which is usually my starting point).
What I do is use Google. . .entering my destinations, arranging them and then exporting the Google map to a KML file.
The import the KML file into BaseCamp.
I next select all the waypoints listed in the new BaseCamp map and create a Route from them. . .using a starting point (my home) and an end point, (the destination) and the optimizing the route.
It seems that each time I import a map, BaseCamp creates a new waypoint in my collection. I think that I could delete ALL the way points in My Collection.

My Collection is simply all the data you have in BaseCamp. If you delete it you won't have any data in BaseCamp. If that's okay with you then go ahead.

Garmin requires unique names for each object of a given type. For example, a Waypoint and a Route named ?Fred? is okay, but two Waypoints named ?Fred? is not allowed.
Each time data is imported into BaseCamp from an outside source, it will check to see if the name has been used, and if so, it will append a number to the name.

If you wish to keep your waypoints and routes, you will have to do some housekeeping. For each duplicate Waypoint, you will need to find out which Routes use that Waypoint. Open the Waypoint Properties and click on the References tab to find the Routes. In those Routes, you will need to insert the Waypoint you want to use and remove the duplicate. After correcting all the Routes used by a duplicate Waypoint, you can delete the duplicate Waypoint.

In the future, you should import your file to an empty list, check for Waypoints with numbers appended at the end and replace them with existing Waypoints if and only if they are at the same coordinates.

It might be a good idea to create a second database (via Options>General) so that you can practice using BaseCamp without worrying about messing up the data you already have.

It might be a good idea to create a second database (via Options>General) so that you can practice using BaseCamp without worrying about messing up the data you already have.

This I will do. Thank you for pointing that out.