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Thunderbird Address Book/Android Contact Groups Synchronization
An Android app and a Thunderbird extension to exchange Address Book/Contacts Group data.
Current version of the app is available on Android market.

Read the help documentation here.

May 28, 2011: Thunderbird extension is Thunderbird 12 compatible.

The free Android app is here.
The Thunderbird extension is here (rename the file to end with .xpi to install to Thunderbird properly.  Right-click the link to "Save Links As...", and change .zip to .xpi).

Yet Another Contact Manager
For Android 2.0+.  Navigate Contacts and Groups with your finger, the trackball or D pad.  Multiple accounts supported.
The app is here.

These apps are also available on the Google Play market.