This is not actually a website, but a technology, and it’s one that will help you keep abreast of as many sites as you think you need to follow.
It’s RSS, which stands for Real Simple Syndication, and it’s an invisible (to most users) technology that “pushes” every post from most blogs and sites to “subscribers.” Many people don’t use this technology; when it was first introduced it was somewhat fiddly, but nowadays it’s very easy and user friendly.
You can view RSS feeds in your browser, or in a dedicated application. We use NetNewsWire, a for-pay ($10) app for Mac. It’s this simple: type the name of a site whose RSS feed you want to follow. NNW will then offer you the choice of available feeds. Most blogs let you subscribe to both posts and comments. We can’t imagine a circumstance in which we’d subscribe to comments: just the five sites on the left from our initial setup of NNW offer more posts a day than we can practically read all the time. And since then we’ve added three more site. So you can imagine how buried we’d be with comments. If you follow many more websites, you can organize the sites into folders for convenience.
Other RSS readers offer different feature sets. A great many of them are free. There are also web-based (as opposed to app-based) RSS readers like Feedly, and as we mentioned, you can set up RSS feeds in some browsers, such as Internet Explorer (if you’re stuck using that, you poor wretch).