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Whether you care about SEO or not, redirect the non-preferred version to the preferred one (www or non-www) using a simple 301 redirection. If you have access to your web server, you can modify the .htaccess file at the root of your site. Google for the exact lines of codes to add (they depend on whether you are redirecting to the www or non-www version).
You can use Google Webmaster Tools to choose a preferred version of site link for Google.
-----Can you comment on whether this is a best practice for all domains?
Yes, it is.
-----I've run a report for backlinks. If my thought is true that there are some pointing to www.www.MY-CUSTOMER-SITE.com and some to the www.MY-CUSTOMER-SITE.com, is there any value in addressing this?
You shouldn't worry about that at all. 301's are just fine. They don't only redirect visitors, search engines like Google also follow them to pass authority signals to the redirected page.