I recently released a new version of Greed, an RSS reader with Google Reader integration. Works like any other RSS reader, except that all your feeds and the actions you take on them (read, star, share, etc.) are reflected in Google Reader, and vice versa. Share items via e-mail or Twitter if you have a Twitter client installed (e.g. Twidroid).
If you want to be notified when certain RSS feeds are updated, you can mark them in Greed, and it will alert you when updates happen.
Greed also features full off-line support. You can download individual files to the SD card, as well as articles, or whole feeds. You can also mark feeds in much the same manner as the notifications described above, and download an offline copy of all new items in the marked feeds.
You can find Greed on the Android Market. Search for "Greed" to see both the free "Lite" version and the Full version for $2.99.
The Lite version does not have offline caching support, the ability to see friends' shared items, or podcast support.