So you like the speed of Google Chrome, but you want a browser that doesn't communicate quite so much data to the borg collective? Because Chrome is built on the open source Chromium project, there are plenty of options for you.

Third-party developers have taken steps, like removing the unique tracking ID Google slaps on each Chrome install, search suggestions, and other bits which communicate various things about you back to Google HQ. Granted these builds don't do anything about the numerous other ways Google tracks you, but they're a decent starting point.
SRWare Iron (pictured)
Iron is the veteran of the bunch, having been developed in Germany shortly after Chrome burst onto the scene. You can read a complete list of what differences exist between Chrome and Iron on SRWares website. Apart from what I mentioned in the intro, Iron also strips search suggestions, the Google updater, error reporting, and a few other features (none of which should adversely affect your browsing experience).

A new version of Iron was just posted on the SRWare forums which is built on the newly-released Chrome 4.0.280 stable code. As such, extensions and bookmark sync are fully supported.

ChromePlus
When ChromePlus first arrived, it was a handy way to get features like mouse gestures and IE Tab -- making it an attractive option for some users. Even with the extension gallery open and those extensions readily available to all Chrome users, ChromePlus' default enhancements (now including 'superdrag' and support for external download tools) still make it a nice alternative. Adblocking is also included in ChromePlus.

Comodo Dragon
It was really just a matter of time before Comodo finally broke down and released a program called Dragon, and here it is. It's a privacy-focused rebuild of Chrome, though it's currently using the older 3.0 codebase -- which means no support for extensions out-of-the-box. It is, however, available in a portable version and it has a few tweaks like improved certificate validation checking. As with Iron, the unique ID, error reporting, Google updater, and more have been removed for privacy reasons.