The Apple hype machine has certainly made some folks treat these as the second coming of Ajax. To me they are in a continuum of evolving JS libraries and frameworks, including Google GWT and such popular libraries as Dojo, JQuery, YUI, and Prototype. I don't particularly expect any one winner to take all, at least not for years, and then only in parts of the Web. On certain devices, of course, you may have essentially no choice, but the Web is wider than any one device, however popular.
Do you think that we are likely to see the death of desktop applications?
No, but I think you will see more desktop applications written using Web technologies, even if they are not hosted in a Web server. And of course Web apps will continue to proliferate. With the evolution of JS and other browser-based Web standards, we'll see Web apps capable of more interactions and performance feats that formerly could be done only by desktop apps. We are already seeing this with offline support, canvas 2D and 3D rendering, etc. in the latest generation of browsers.
Flash is doing its part to be a good "Ajax" citizen, to be scriptable from JS and addressable using URLs -- to be a component on the page along with other components, whether plugins, built-in objects such as images or tables, or purely JS objects. The open Web levels everything upward, and militates against single-vendor lock-in. You can see this in how Flash has evolved to play well in the Web 2.0 world, and Microsoft's Silverlight also aims to integrate well into the modern Web-standards world.
People fear a return to proprietary, single-vendor plugins controlling the entire Web page and user experience, but I doubt that will happen all over the Web.
First, Web standards in the cutting edge browsers are evolving to compete with Flash and Silverlight on video, animation, high-performance JS, and so on.
Second, no Web site will sacrifice "reach" for "bling", and plugins always lack reach compared to natively-implemented browser Web standards such as JS. Users do not always update their plugins, and users reject plugins while continuing to trust and use browsers.
Certainly in the browser, but also beyond it, in servers and as an end-to-end programming language (as well as in more conventional "desktop" or "operating system" scripting roles).
Do you still think that (as you once said): "ECMAScript was always an unwanted trade name that sounds like a skin disease"?
I don't think about this much, but sure: it's not a desired name and it does sound a bit like eczema.