What’s the simplest way to add paid memberships to a consumer website?

There are many such sites (the term you are looking for is membership sites):

• SubHub (www.subhub.com)
• MemberGate (www.membergate.com)
• ExpressionEngine (their software has a membership engine, this is for developers who build and deploy their own website: http://expressionengine.com/over...)
• MemberWing (a WordPress Premium Plugin for Premium Content: http://www.memberwing.com/)
• SquareSpace (another hosted website development tool, that has site membership options: http://www.squarespace.com/featu...)
• MemberClicks (http://www.memberclicks.com/)
• Kajabi (http://www.kajabiapp.com/)
• MagicMembers (WordPress Plugin for Membership Sites http://www.magicmembers.com/)

Do look at Chargify for recurring or membership billing (See http://chargify.com/third-party-...).