The GitHub API is pretty damn close these days, and I can tell you that there's a very big company you've heard of with a two-digit person team working on a HAL-based hypermedia API right now. Twilio has been pretty good too.
There are lots of private APIs that operate this way; for example, much of Comcast's internal stuff is pure, hypermedia driven REST. But it's not open source, so you don't hear about it.
A YC-funded company, Balanced Payments, does an excellent job as well.
> those seem too fundamentally different from any API I might create.
Right! That's because you're primarily thinking of RPC styles, so of course it will seem foreign. Try this sentence on for size, from a different time period:
"But who has truly object oriented objectives in mind? Some people tell me that Smalltalk or C++ are examples, but those seem too fundamentally different from any code I might write."
That's not to say RPC is a bad thing: often times, it's just fine. But if you have the problems REST is designed to solve, REST will solve them much better.