Mac only: Previously mentioned NetNewsWire is currently the premeire Google Reader-syncing RSS client for Mac, but free app Gruml may give it a run for its money, adding many Google Reader features too, like sharing and sending articles to many other services.
While NetNewsWire is definitely a great app, RSS addicts will definitely want to check out Gruml as well, especially if you're a Google Reader Fanatic. While NetNewsWire is a great RSS client, Gruml specifically attempts to be a Google Reader client. They have very similar layouts and experiences, but Gruml adds tons of Google Reader features to the client that NetNewsWire doesn't have, like following people, recommended items and sharing. Also, instead of sending articles to a limited number of other apps (mainly Instapaper, Twitterific, and Delicious), you have the option to send articles to a huge amount of services, like Digg, Facebook and Evernote.
The app is still in beta, so it's not quite as polished as NetNewsWire (NetNewsWire still looks a bit more Mac-like), but it's pretty darn close. And, if you're a hardcore Google Reader fan, you can't go wrong with having all those extra features in your client, thus saving you the trouble of going to the webapp just to see what your friends have shared. Note that you do not, however, have some of the other advanced features of NetNewsWire like smart folders, so you'll need to decide which is more important to you when deciding which app will win your love.
Gruml is a free download, Mac OS X only.