What do you use for your feedreader?
You set up your subscriptions as either "Kindling" or "Sparks". Kindling are your essential feeds and Sparks are your supplementary feeds. So Sparks just kind of sit in the background (though you can read them too), but when enough of them start pointing at an interesting story, that story becomes "Hot" and is prioritized by "temperature", kind of like Techmeme does, but for your personal feeds. It has completely wiped out my "Unread Items" issue, because that number isn't really surfaced in the UI. And with the Hot items, you're unlikely to miss something important.
It has folders.