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The best app for Android tablets was only recently released, and only for devices running Ice Cream Sandwich. While not many can use Chrome Beta as a result, it is easily the best browser for Android.
Chrome looks and acts just like the desktop version, and if you use Chrome there you will absolutely love it on an Android tablet.
Free on the Android Market
See full Android coverage by James Kendrick on ZDNet Mobile News
I'm a sucker for a good title bar on Android devices that has a good clock and weather information. My favorite for tablets is HD Widgets, a set of home screen widgets that displays just what I want.
The clock and weather section is configurable, and in different sizes to only take as much room as you want to give up. The bar resizes automatically when the tablet is rotated.
$1.99 on the Android Market
Honorable mention: Beautiful Widgets