I still use an RSS reader (Feedly) for much of my news. It's the best way I've found to aggregate all of my sources in one place. But for a few sources (including my own organization’s news feed), I want to know immediately when something new is posted.
I did some research of various services, and the one I ended up using and liking best is RSSFWD.com.
It's run by an email marketing platform called Campaigner. which I don't use. But I do love companies that provide useful tools to the world for free. So giving them a shout out as a company worth checking out if you are looking for email marketing. (Definitely don’t go with Vertical Response.)