For those who just would rather get stuff via email, there are applications like Blogtrottr that allow you to subscribe to feeds, but get new posts sent to your email box. Many blogs offer a "send to email" option as well. In addition, Microsoft Outlook (2013, 2016, Office 365) have built-in feed readers that treat blog posts like email (you can even see blog posts in the web version of Outlook). Note: You can read blog posts in online Outlook, but you can't add new feeds/sites.
Although it is still an important web tool, these days its more on the back end for most people.
Except...podcasting
My Yahoo My Yahoo is a popular portal that integrates feeds and other content.
Years ago, many people used Google Reader for their RSS feeds, but that service is no longer available. Many people switched to the Feedly RSS reader service. You can find an updated (2021) list of recommended feedreaders here.
How to Find or Create an RSS Feed for Any Website (via HowToGeek)
Facebook used to have (and may still have) dedicated ways of incorporating RSS feeds into your Facebook feed but now mostly focusses on having you Follow or Friend the blogger or Like the blog's Facebook Page... See also: Twitter, LinkedIn, etc.(the "statusphere") ; Pinterest ; Instagram, etc.
For mobile devices: FlipBoard, Google Play Newsstand, Apple News, etc
Issues with Sharing on Social Networking Sites... (see also: this article about archiving the web via Twitter)
This article focuses on Twitter, but you may find similar results on other social networking sites. There is also the issue of actually *locating* a link or post you shared or found on a social networking site! And of course, the problem of sharing things on your social networks unintentionally...
...Problems