Organize template parts and page templates in folders in regards of template hierarchy

Page templates are special case and since WP 3.4 can be put in subfolder natively. Other than that WP mostly expects flat file structure for templates.

While template hierarchy is easily adjusted (see dynamic filter in get_query_template(), pretty much only thing needed)… From personal experience – overly extensive and nested directory structure for templates makes developer workflow overly unpleasant very fast.

If you have extreme quantity of templates “how to reduce amount?” is better question than “how to stuff them into folders?”.