The closest equivalent community license that I can think of to a Sites license is the High Volume Customer Portal (HVCP) license. It's a volume/use-based license that was originally used for Service Portals. It's sold based on an average monthly usage with allowances for peak monthly usages that go well above the average to accommodate seasonal needs (like Christmas or other major events in your cycle).
See About High-Volume Community Users for more on this license and it's limitations. One very important thing to recognize is that these users won't have access to Opportunity and some of the other CRM Objects in a community that users do in other types of communities. They will however have access to their Account information and any custom objects that you set up for them. They can't own records and all records are shared with them via groups or through "implicit" sharing (primarily via the user's owner).
Yes, You can access communities without logging in. Its called as community guest user license or non-authenticated community users.
You can even create/update records of some standard/custom object.
But .... Its more restrictive with respect to limits in usage...
Non-authenticated community users have 1,000,000 page views per month or at max 60hours of server time per month(Unlimited License)
Once you log in, the limits dont apply as its translated to perfect community partner/customer user license.
So yes you can do few things(read ugly hacks), like create custom user object to create/maintain your own session,create own login and do extra functionality without using any standard customer community license if Overall community limits are not surpassed.
Note: Creating custom userObjects and faking sessions posses security risks as none of the salesforce security protocols apply and you have to implement security on your own. I don't know if that comes under license abuse.