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Gmail for Honeycomb is so good it may be reason enough to buy a tablet for power users. It makes good use of labels and starring to keep your email organized and accessible. Visit ZDNet Mobile News for the complete picture of top Android apps for tablets.
Twitter apps are a dime a dozen but good ones not as easy to find. Plume (formerly Touiteur) has been optimzed for Honeycomb and is a joy to use. It rivals desktop Twitter clients in the way it displays multiple columns of the user's choosing, and packs in great touch optimization to round out the offering. There is both an ad-supported version that is free and a premium version.