Is there a way to populate a drop-down with the templates files in a folder? When I have a folder setup for template partials, is there a way I could automatically populate a drop-down with the list of templates in that folder?

This would be useful in the case where I have a complex matrix field set, and would like to select a partial to render or include along with the block's content. 

If the drop-down were automatically populated, it would eliminate a lot of time setting up the drop-downs in the backend, and would make it much easier to deploy new feature sets across many Craft based sites as they are developed or improved.
This would be a good task for a plugin.

You'd essentially need to build the plugin to do a couple of things:

(1) Use PHP in a service to list the contents of a directory. Once you have that list, you'd then need to...

(2) Deliver that information to the front end via a custom field type. You can then use your new custom field type wherever you'd like.