> Inoreader (paid pro version) will also allow you to create feeds for sites that do not publish via rss.
I am a paid pro subscriber on Inoreader, and use it 2-3 hours a day for my work. I should mention that it provides a very limited number of certain types of feed (custom-created RSS, Twitter feeds, etc.), and you'll run out of them almost immediately if you want to follow a lot of places.
That said, Inoreader lets you plug as many RSS feeds as you like in, far as I can tell, and I've really loaded it up.
But do watch out for the limits, because the next grade up from 'Pro' is 'Call sales'. It's not very granular.