*NOTE: This is not feasible as of the latest SFDC Releases. *
Specifically we would like to remove the ability for the users to add Notes to an object, but still retain the ability to add Attachments.
You cannot remove the button from the Notes & Attachments related list via standard declrative features (Page Layouts, etc). We would like to remove the "New Note" button, as well as rename the Related List to "Attachments".