> Maybe we should switch all these to "awaitable"?

I like this!  Would it be OK to add a new sphinx declaration?  So that:

   .. coroutinemethod:: AbstractEventLoop.shutdown_asyncgens()

would become:

   .. awaitable:: AbstractEventLoop.shutdown_asyncgens()
   
?

> Also note that in proactor_events.py, sock_connect() is *not* a coroutine. 

Yeah, those small incompatibilities are inevitable for asyncio programs/frameworks -- something that returns a Future may occasionally become a coroutine.  Your idea to document API methods as "awaitables" seems to be the right way to go.

> In fact I'm not sure what it is -- it calls self._proactor.connect() which appears to return None from the code in windows_events.py. That's presumably a separate bug.

It looks like it returns the result of "IocpProactor.connect()" call, which returns an _OverlappedFuture instance (I don't really know Windows part of asyncio code, so I might be missing something).