I use rawdog. It runs on my computer and generates a single HTML file, which contains a nice unified list of articles (rather than the common alternative, a list of feeds which I then have to drill down into). It doesn't rely on any external services other than the feeds themselves. By diddling with the template it uses to generate the HTML, I have given it a little interactivity (e.g., I can tell it to "collapse" some feeds so that they show only article titles rather than content; I can then un-collapse individual articles).

Last I checked, it didn't work on Windows but could be coerced into doing so by fiddling with the source code (it's in Python).

There is a thing called Tiny Tiny RSS that, from what others have said, I suspect may offer kinda-similar functionality but better (with perhaps a bit more effort to get it set up initially). I keep meaning to check it out but failing to do so.