I love to use RSS reader software, it supports my collection of favorite news sources, track and store every day, it is one of the indispensable software for me.
I know some software / service features are attractive, meet the requirements of most users, however, depending on preferences that people find it preferable to another.
Here are some softwares/services which I have used over and feel it has some hightlight features.

Greatnews (Windows)

GreatNews is a RSS feed reader that optimized for fast and efficient reading of your favorite web feeds. It offers different view styles, including a newspaper view, that allows you to read a group of feeds organized arranged in newspaper-style page layout without having to click through individual feed items.

Greatnews

The program supports custom labels, email and blog integration as well as custom keyword alerts (news watches) that let you automatically find articles of interest and have them available in a special category. Other features include import/export feeds from/to OPML and XML files, automatic cleanup of old items, browser integration with popup blocking and more. GreatNews is small, fast and very efficient - it does not require an installation, just unzip and run.

Sage (Firefox extention, Windows, Mac OS)

Sage is a lightweight RSS and Atom feed aggregator extension for Mozilla Firefox. It's got a lot of what you need and not much of what you don't...

• Feed Discovery
• Integrates with Firefox's bookmark system
• Imports and exports OPML feed lists
• Newspaper feed rendering customizable via style sheets
• Support multilanguage.

Sage

NetNewsWire (Mac OS X)

Looking for an easy-to-use RSS and Atom reader for your Mac? You’ve found it! The Eddy-award-winning NetNewsWire has a familiar three-paned interface and can fetch and display news from thousands of different websites and weblogs.

NetNewsWire (Mac OS X)

One of NetNewsWire's best and most unique features is its Smart List feature, which works like iTunes' Smart Playlists: it creates special watches for important topics or authors you don't want to miss. The downside of many desktop readers is that there's no online access, but NetNewsWire syncs with the online newsreader, Google Reader, and back again, so you're never without your feeds if you've got a browser.

FeedDemon (Windows)

FeedDemon's interface is very good, but its default setting, which places the headline and browser panes side by side, is somewhat clumsy. This is easily remedied with the buttons that sit right at the top of each folder and each item. The utility's Watch Channels feature searches for news items containing user-specified keywords and places them in a separate group so they're easier to find. We're also fond of the app's News Bins function, which allows you to archive a story simply by dragging a headline and placing it in a storage bin in the left-side column.

FeedDemon (Windows)

FeedDemon, the most popular Windows RSS reader. The easy-to-use interface makes it a snap to stay informed with the latest news and information. You can completely customize the way feeds are organized and displayed and set up custom news watches based on keywords. You can even download podcasts and audio files and have them show up on your portable audio device

Google Reader (Web-Based)

Google Reader is a Web-based aggregator, capable of reading Atom and RSS feeds online or offline. It was released by Google on October 7, 2005 through Google Labs. Reader graduated from beta status on September 17, 2007.

Google Reader (Web-Based)

Google Reader has impressive speed and usability. The most obvious benefit of an online reader like Google Reader is that no matter whose computer you're using, you can access your feeds from the same interface, with the same items read, unread, starred, and tagged, as long as you've got a browser handy. Aside from that, Google Reader really gains loyalty with its robust keyboard shortcuts, search, and tagging features.

Bloglines (Web-Based)

Bloglines is a FREE online service for searching, subscribing, creating and sharing news feeds, blogs and rich web content. With Bloglines, there is no software to download or install -- simply register as a new user and you can instantly begin accessing your account any time, from any computer or mobile device. And it's FREE!

Bloglines

Bloglines shields you from the confusion of news feed standards -- RSS, Atom, and others. Bloglines allows you to search for, read and share any updates from your favorite news feed or blog regardless of its authoring technology. And it's FREE!

Vienna

Vienna is a freeware, open source RSS/Atom newsreader for the Mac OS X operating system. It provides features comparable to commercial newsreaders, but both it and the source code are freely available for download.

Vienna RSS Reader

Vienna RSS Reader is a true Mac OS X application. The whole effort to install the application is to copy it into the Applications folder. After installation you can do the basic setup of the reader and then you can start to browse the Internet to start adding the RSS Feeds to the Vienna RSS Reader.
iGoogle, Netvibe, ... and the similar website will not list here 'cause it is not really feed reader.
In this article I'm not  rate for the best software because each person has a habit of using different software, GreatNews which I used to, it has feed database is stored in a simple SQLite file, compact, light and portable while FeedDeamon software is another favorite.