The long and the short of it is this:
- There are a number of Google services that you can use -- including Chrome, Search and Youtube, to name but three -- that you don't have to be logged in at all to use.
In regards to Android specifically, the good people in Washington asked for the following:
8. Please explain exactly how a user of an Android Phone will be affected by Google’s new policy. Is there any ability for users to opt-out, other than not purchasing and using an Android phone? How will Google’s new policy affect users who do not use an android phone but automatically stay logged into their Gmail accounts on their phones?
Here's Google's full response to that question:
Users can choose not to log into an Android phone with a Google Account and still use it to place phone calls, send text messages, browse the web and use certain Google applications that do not require account authentication such as Google Maps. Some Google applications such as Android Market and Gmail require authentication with a Google Account.
Be sure to hit the links below and read Google's complete responses.