Here are 5 of the most popular, standalone feed reader applications for Linux. I didn't include feed readers which come with applications like Firefox, Opera or Thunderbird for example, but these can also be considered a viable alternative to the ones below.
Liferea developers have announced the availability of the first stable version of the 1.6.x series. Liferea (Linux Feed Reader) is an aggregator for online news feeds. There are many other news readers available, but these others are not available for Linux or require many extra libraries to be installed.