There are a few RSS reader clients for the BlackBerry PlayBook but there is a couple that stand out. One of those is GeeReader a free RSS reader that syncs with your Google reader account. With the latest update I noticed that it Syncs your read articles to your Google account. The client is free and is one of the most responsive applications.
GeeReader is a touch-optimized Google Reader client for the BlackBerry® PlayBook™.
Sync directly with Google Reader to retrieve your RSS feed subscriptions
Use your Google account to login.
Star, Like, and Share feed items.
Mark all items in a feed as read.
Sort feed items by "Newest First" or "Oldest First".-
View the article detail in a maximized window by tapping on the article detail panel title bar.