NewsRob offers two different flavors, the free version and the pro version. The pro version adds some features that are more specific to power users, and removes the ads. My suggestion is to go for the pro version after you've tried the free version for a few weeks. You're going to love it.
NewsRob requires you to have a Google Reader account, and allows you to log in with those credentials. All this happens securely as NewsRob never stores your password. Once set up, the 50 latest articles will be downloaded and made available to you, and this is where the fun starts.
NewsRob has an almost unlimited amount of features, allowing you to download up to 1,000 articles, and store them offline on your device. This can be either on the phone’s memory or a storage card. Offline storage comes in different flavors as well. You can either save the feed only, or have NewsRob reach out to the web site and download the entire page. This is the power of NewsRob: it gives you the flexibility to read feeds offline when you don’t have a network connection.
Another killer feature is the scheduled sync. You can tell NewsRob to fetch new articles a few times per day, keeping your reading list current. This also syncs back to Google Reader, making sure you don't read the same articles twice. NewsRob also gives you the option to share or annotate an interesting article with others.
After trying several other RSS apps, NewsRob is the big winner. Five euros is well-spent, and the responsive developer is always interested in hearing what you think can be improved.