There were specific RSS feed readers but they gave way to using your browser or your email client might have a function for following RSS feeds.
Well with Google testing RSS feed subscription in Chrome it might be the right time to reconsider adding a RSS back on your site.

RSS 2.0 specification (at W3C)What is RSS?
RSS is a Web content syndication format.
Its name is an acronym for Really Simple Syndication.
RSS is dialect of XML. All RSS files must conform to the XML 1.0 specification, as published on the World Wide Web Consortium (W3C) website.
Does your site have a RSS feed?