Well, any web browser in private mode, with a Google tracking blocker, will block Google's tracking. AdBlock and Ghostery plugins are available for most every browser, and the pair will stop almost every tracker out there.
There is no such thing as TRULY anonymous web browsing, though. Even TorBrowser has vulnerabilities that can 'leak' your info. Opera has the benefit of built-in VPN IP-hiding in its private mode, though. For the simplest "pretty good privacy" (no relation to the actual PGP) Opera's probably the easiest/most private. But any browser can be made more private with tweaks.
Also, for maximum privacy, don't log in to any website, ever. Don't participate in any web forums. Don't post a comment on anything. Switch web browsers constantly, switch OSes and CPUs too, if you can. Only browse from someone else's (secure) WiFi, not from your own house/work/school, use a VPN/Tor/etc. Reformat your computers regularly.
Or, for maximum internet privacy - stay off the internet.
Really, it's a matter of deciding what level of privacy-to-convenience tradeoff you're willing to make.