I've been reading up on web components and am pretty intrigued by the nascent spec. Does anyone know if there is any support for 2-way data binding in the DOM, without having to use Polymer? An example would be appreciated.
No, data binding isn't part of the Web Components spec.
You can of course implement data binding yourself using native JavaScript event listeners, and possibly the Proxy object, but it's probably best not to re-invent the wheel: if you want data binding, choose one of the many JavaScript frameworks out there which supports that. Polymer, React, Angular, and Vue are some recent examples of such libraries.