True to the non-linear nature of interactivity, this isn't a true hierarchy. More of a bag of interrelated goodies that you can mix and match. Nevertheless, they are listed in the order of increasing impact.
1. None. Just a book. Nothing wrong with that.
2. Decorative. Added video or 3D models where illustrations would do. Links used as simple references. (Most 'enhanced' e-books.)
3. Functional. Important parts of the book require interactivity. (Apple's .ibooks textbooks. Voyager's expanded e-books.)
4. Structural. Interactivity is integrated into the book's structure. (Books with extensive cross-references. If Monks had Macs. Afternoon. Patchwork Girl. Solar System. Skulls. The Elements. The Wasteland.)
5. Networked. Outside meaning enters into the book, surrounds and frames parts of it. (Kindle notes and popular highlights.)
Most attempts at e-book interactivity over the last few years have been decorative. Add a few videos and gloss to an established text, raise the price, and hope nobody notices that it's a lazy ripoff. Most of the e-reader platforms allow for this kind of interactivity, at least to a limited extent.
With Apple's announcement of the .ibooks format we've begun to see renewed interest in functional interactivity, where widgets add substantially to the meaning and important parts of the text are delivered through interactivity.
Structural interactivity is the kind that is the most difficult to implement and has drawn the most attention.
How difficult is it in practice? Most of the major titles of this type come from a single developer: Touch Press.
Most developers misunderstand networked interactivity. They almost always take it to mean that data can be pulled into the book and the book changed in some suitable way.
What it actually means is different: Networked interactivity is about re-contextualizing data.
Most of the time this means data that's pulled from or pushed into the network, but that's not a requirement of the basic concept.
These types of interactivity are easily implemented on the web with standard tech but the situation in e-books isn't nearly that simple, for a variety of reasons:
The complete absence of developer documentation or tools in the e-book field is a large part of what makes app- or web-based interactive books so attractive to publishers. Add to that the iPad's large, relatively uniform, and paying user base and you begin to see why so many 'enhanced e-book' efforts begin and end with native iPad apps.
If you're going to go proprietary, you go for the largest, best documented, most productive platform around.
(This ties in with my earlier theme: e-book platforms are competing with other platforms, both for talent and for customers. A publisher's biggest enemy isn't Amazon but Angry Birds.)
Approaches and tactics for e-reader vendors, publishers, and readers need to be considered separately.