Android (4.0+): Flow Reader may be in beta, but it's already one of the best news readers we've seen for Android. It delivers your feeds to your Android device quickly, syncs with Google Reader, and gives you options to filter out stories.
Flow Reader's biggest benefit is in its simplicity. It doesn't move stories around trying to predict what you want to read, but it does use its own algorithm to remove "sponsored" stories and ads inserted into RSS feeds so you get a clean reading experience. It saves stories for offline reading, and you can filter articles by read, new and unread.
Plus, Flow Reader lets you filter articles by author or specific topics. The app is still in beta, so you may run into some bugs here and there -- the developer admits this and specifically requests that you report them so they can be fixed. It's free and available now at Google Play.