What is the most widely adopted aggregator or RSS application?
This is purely a matter of personal taste. You can use all kinds of RSS editors and aggregators. Most are free, and some are not. Usually there's not much of a difference between the free and the not-free. I myself use "Feed Editor". I find it does what I need it to do, namely create an .rss file that I can upload to my free webhost. From there, it depends what I want to do with it. I often use http://www.sproutbuilder.com/ to create a widget that uses it.
A widget is a little software gadget that you can put on your webpages. Widgets perform a function of some kind, like perhaps a calculator, or a little calendar for the month. Sprout allows you to create little widgets for your websites that can do all kinds of nifty things, without any programming knowledge or experience. You point, you click, and that's pretty much it. One of the things it can do is take an RSS feed, and display it graphically in a little box you can put on your webpage. I've taken RSS feeds from various online news sources, an eBay search I check a lot, and for Free Stuff listings for Craigslist in my local area, and put them all together on a page. This should give you a good example: http://satori.110mb.com/Satori/Images/cheatsheet.htm
I should also mention that many websites generate an RSS feed automatically. Look for the little orange box, usually somewhere down at the bottom of the main page. RSS feeds are just a more widely-used variant of something called Atom publishing. You may want to check out the Wikipedia article on it.