Even after the death of Google Reader, I've been an avid RSS user for many years, most recently using Feedly. RSS is a simple feed for web pages, and an RSS reader aggregates those feeds into a single location. I follow hundreds of blogs this way, but more than that. I can follow the updates to a pending state law on the legislature's website, the columns from an opinion writer at a newspaper, or an agency's updates in the Federal Register. And unlike Twitter (where I probably have to see it pop up at the top of my feed, and the author must actively share the piece) or Facebook (where I might be stymied by the News Feed's proprietary algorithm that only lets me see certain content), I get to see everything, and everything is held until I open my reader and peruse the headlines.
Yes, RSS can be a bit wonky to the average user, but it's an essential way for me to gather news. That includes federal appellate judicial opinions. Below, I've aggregated the RSS feeds of each of the federal courts of appeal. When given the option, I chose all opinions instead of only "published" or "precedential" opinions. When given the option, I also chose the "summary" or "daily" option that aggregated all the day's opinions into a single RSS item rather than ones that would separate them into independent items. In the event you find a better feed or an error, please let me know!
Second Circuit (no longer operating)
Sixth Circuit (no RSS, only email subscriptions)
Federal Circuit (no RSS)