My favorite way to catch up on websites has been to use Google Reader. Sadly Google has canceled this once-fine product, and it's shutting down on July 1.
Several substitutes have emerged, and I've tried them all. My favorite is FeedBin. It costs $20 a year, and it's well worth it. It's got a very good web client, and it syncs with Reeder, my favorite iPhone feed reader.
It's easy to export your feed list from Google Reader:
And like that, all your feeds are imported! Now is a great chance to go through them and remove the chaff that has accumulated over the years. Press "?" at any time to see a list of helpful keyboard shortcuts.
On a related note, we are also switching the location of our feed from Feedburner to http://www.unshelved.com/feed. Please update your reader. The old address will continue to work until Google shuts that down too.