SSL makes a difference.
See correction below:
Google doesnt care, but it may be a waste of your bandwidth.
The common approach is to use non SSL on pages where data is not entered into forms or form values are processed and SSL on pages where they are.
Google sees an https://
and http://
request as the same. But will see the www.example.com
and example.com
as two seperate sites.
Most sites just use the https://
on pages where user logs in, gives credit card, edits his/her information, etc. On pages where someone just reads information such as home page, or terms, or privacy policy, blog artices and so on its best not to force HTTPS.
Correction - 1/23/15
as of August 2014 Google prefers
SSL http://searchengineland.com/seo-industry-tweets-reactions-googles-ssl-ranking-boost-199510