I am a wildly devoted RSS reader, and it's how I get probably 80% of the non-Youtube non-Podcast* content I see on a daily basis. I love being able to scan through dozens of sites I follow and pick out the stuff that's interesting, and RSS makes that possible and relatively easy!
Personal picks: I use Feedly as the place that stores all my subscriptions, and use its site on the web + its iOS app on my phone, and then switch to Unread for feed reading on the iPad (which plugs into Feedly so everything syncs.)
That said, the other 20% does come from Twitter.... but via Nuzzel, a neat app that aggregates links shared by the folks you follow and surfaces the stuff that is most popular. RSS is great for seeing everything, and then Nuzzel catches whatever is hot at that particular moment that may come from outside of my chosen feeds.
*Asterisk being that all podcast feeds are actually RSS feeds, so honestly basically Youtube is the only outlier.