I use Google Reader, which is good for me since I read from two computers and from my phone. I noticed nobody recommended it...do these dedicated feed readers do cool stuff that Google's reader doesn't?
Well, Google Reader is an online reader using the web browser. Many of these apps integrate with Google Reader's feeds, but it's a little different.
FeedR, the one I recommended, integrates with all of my Google Reader feeds. That way, I can read my feeds with Google Reader when I'm in front of a computer, but my phone also downloads the feeds once an hour, so I can read them offline. All feeds marked as read on my computer get marked as read on my phone, and vice versa.
Plus, unlike the web browser, I get real application flexibility like being able to change fonts and font sizes, set it to white text on a black background which is easier on my eyes, I can color code feeds so I know what category they're in, get notifications if I want, that kind of thing.
I use Google Reader on my computers, but being able to set it to white-on-black on my phone is worth the application by itself. Also it stores them offline, so there is no waiting and I can read them even with no network access.