Feed Readers

I also maintain a review of feed readers at Gizmo's Tech Support Alert, along with reviews of a couple of video and audio feed readers. You'll find more on readers in my topical links too.

Web-based feed readers

Web-based feed readers (aggregators) give you an easy way to start reading feeds. Think of them as "Web-mail for RSS". Nothing to install, and you get instant gratification. :-) Most of them also provide a way to search for feeds on topics you're interested in.

Google Reader is simple enough for beginners, yet fast and powerful enough for most others. I like the way it integrates seamlessly with tabbed browsing, and its "J"/"K" and "V" keyboard shortcuts make it easy to skim *tons* of feeds.
Netvibes is an nice online feed reader, which also offers a wide range of "widgets" for accessing other kinds of dynamic content.
Original Signal — not exactly a feed reader, but it will give you an instant feel for what you get with feeds. Don't be distracted by the geek oriented content. :-)
Gmail and Yahoo! Mail, both include feed reading, as do many email clients like Thunderbird.

Browser- and Web-based readers have a big, but not so obvious advantage over desktop readers. Since they run in your browser, it's easy to open links you find in the posts directly in other tabs right in your favorite browser. It's also easy to keep the browser controls from using a big chunk of your display. Just hide your browser's "chrome" (toolbars, etc.) by using the "F11" function key to toggle between normal and full screen view. :-)

Browser-based feed readers

All major browsers now include easy-to-use basic feed reading. You can also beef up your browser's native feed reader — particularly Firefox — with add-ons.

You can read feeds directly in IE, but the best choice is a compatible desktop reader like RSS Bandit, or use Windows Live Mail. Both of these synchronize with the "Windows Common Feed List".
LiveBookmarks for Firefox provides basic feed reading. If you want something less basic, the Brief extension for Firefox is "Designed to be easy to use and streamlined, with exactly the right set of features." Brief integrates fully with Firefox's Live Bookmarks.
If you're looking for something more versatile, try the NewsFox add-on for Firefox, which also integrates with Live Bookmarks. There are more ideas for reading feeds with Firefox at the Firefox Facts blog.
Desktop feed readers

"Desktop" feed readers (they also work with laptops) are stand-alone programs that include a browser. (It's usually IE or Firefox in disguise.

FeedDemon

FeedDemon is a powerful, well-designed feed reader. (And it's now free.) FeedDemon is a power user's dream, but it's logical enough that any patient user can learn how to use it. Its the one I use..
FeedDemon integrates seamlessly with Web-based Google Reader, so you can read your feeds at home or away (on the Web) and keep the read/unread status in sync. FeedDemon has very good security, both for feeds and enclosures (feed attachments). [using FeedDemon] [FeedStation]
Other Readers
Some email programs, like Thunderbird and Windows Live Mail, also have built in feed readers. It's very easy to set up feeds in Thunderbird. [Use "Tools" > "Account Settings..." > "Add Account" > "RSS News and Blogs".]
RSS Bandit and Awasu are comparable to FeedDemon, but they're a bit less capable and complex. That means their learning curves are not as formidable. Even so, they are elegant full-featured readers. RSS Bandit is now an Open Source program. It also synchronizes with IE7's Windows Common Feedlist (Vista and XP-sp3). Awasu is widely used by business users.
If simplicity is important to you, check out RSSOwl. It's a simple, straightforward reader that may meet your needs nicely.