Recently, Loren Brichter re-raised awareness of the privacy implications of using the Google Chrome/Chromium browsers and created the Chrome Is Bad website. I suggested using the excellent Opera browser as an alternative for developers.
For iPhone and iMac users, I'd strongly recommend using the DuckDuckGo browser as your default browser. It's a great way to ensure no one can track you on the web.
For sites that you want to remain logged in on, just use the Safari browser. That way, your authenticated / regular use web sites are completely siloed from your generic / on-the-fly browsing.
Here's a demonstration of using DuckDuckGo iOS to keep your browsing private.