I too use Google Reader (although I used to use Bloglines.com). Both these products are web-based readers, which means you typically don’t download the content to your machine, you just read them online. I use many different machines throughout any given day, so the online aspect is one that I very much appreciate.
A few months ago, Google Reader also introduced an offline reading feature, which allows you to download your latest feeds to your machine (say, for reading on a plane). The next time you connect, your feed status is updated / synchronized.
If you’re 100% sure that all you want is offline reading, you can explore some of the mail software products (for example, Outlook 2007 can track RSS feeds). I’m less familiar with this area, though.
If you listen to podcasts, you’ll find that most of them also offer their episode feed using RSS, which you can subscribe to using iTunes.
Speaking of podcasts, if you are in the habit of listening to them, there’s a recent episode of New Comm Road by Bryan Person that talks about Google Reader. The relevant segment starts 7 mins 17 sec into the recording.