Seems everyone is recommending their preferred feed reader here so I'll mention the one I use as well.

Feedbro is a Firefox extension that lets me subscribe to and read feeds. Multiple layouts/formats.

I use it to subscribe to blogs, github repos etc.

I still miss a feature from the Googlr Desktop Search sidebar where it would autosubscribe/unsubscribe to rss feeds as you browsed around the web. I think it looked at what sites I visited, tried a few entries in the feed and continued/canceled based on if I read them or not.