Bill Scott's The SHiFT from the Page to the Application presentation at SHiFT 2006 described a way to classify and understand the interaction design patterns emerging in Web applications today.
Bill organized these patterns along the three dimensions of the Web: Interaction, Feedback, Information. Interaction needs to be tied to information access in order to be useful. As a result, it's relevant information that really enables rich interactions. As Bill pointed out, drag & drop, animation, and other rich interactions were available online before Ajax. But it was the instant access to data that Ajax enabled that really drove the practical use of rich interactions.
Bill's slides are available online and contain examples of his principles for rich interaction design: make it direct; keep a light footprint; cross border reluctantly; give live feedback; offer an invitation; show transitions; think in objects; show transitions.