I would like to specify that I only mean content here - not presentation. So imagine there's just plaintext and browsers are not capable of displaying anything else but it.
Of course we all know that a well written documentation in general is such a rarity in this world and there are, in truth, very few examples (FreeBSD comes to mind) of documentations that stand out simply because you can sense every single sentence was written by a human passionate about it and a human caring for his reader. But how to achieve that - is quite a different question too. Let's suppose this wonderfully written documentation is there.
How does one punch through the wall of indifference with just the title, a subtitle/tagline and one paragraph? What makes you care all of a sudden, even though a minute ago you couldn't even imagine you'd want to try this piece of software or at least read more about it?
Close second is formatting: I really like projects that start with the hook (usually an image of the software in use or an "elevator pitch" of what it's trying to solve), follows up with a list of features, capabilities or FAQ, and then finishes with the less salient info like contribution instructions, build instructions, and general how-tos.
I think upfront it's worth noting that you probably don't need people to "keep on reading" your entire README, in an ideal world you're able to convey the important details first and address more granular issues in a structured and easy-to-parse way. YMMV, but that's my two cents.