This just gets more and more interesting. Apple just rolled out Safari 3.1 and by all accounts it's fast, it's good, and it's basically an RIA platform complete with video and animation support (and offline storage). There are a lot of other things that go into plugins like Silverlight and Flash but Safari is the first browser to really start pushing the envelope around the HTML5 spec which enables things like video and CSS animation and really push HTML into a richer spectrum.
So now I think it's safe to say we have three major RIA players: Apple, Adobe, and Microsoft. Mozilla also continues to innovate around Firefox with things like offline storage and Prism but I'm not sure they have a "rich" direction quite yet. Safari 3.1 may be a smallish blip on the radar overall, but it's a big, big shot in the battle for RIAs. If there's one absolute guarantee here, it's that the web is going to get a whole lot richer and that's always a good thing in my mind.
Update: I can't believe I forgot to mention this but j.m.galvin commented below that the majority of this work is in WebKit which is an open source project. Adobe uses WebKit in Adobe AIR and while I'm not sure what our plans are to incorporate the changes, the fact that this is all open source is a very good sign.