People who read this blog know that I'm not big on building full web applications in Ajax. While the new Yahoo Mail looks really awesome, I think development time would have been much faster using Flash or OpenLaszlo, and would make for a much better experience as Yahoo incorporates multimedia and other content into the mail reader. The only downside to Flash is that it handles text badly, and since an email is all text, you have to code a lot of workarounds to get it working - which is probably why most mail clients are written in Ajax.
However, Ajax, when used for the right application, is the perfect solution. And to show that I'm not just an Ajax hater, I wanted to point out what I think is the perfect Ajax application - Joe's Goals. It's simple, it's efficient, it doesn't require any bells and whistles, and it makes good use of Ajax without overdoing it. This would be a terrible Flash application, because it's meant for a "quick in, quick out" scenario. You don't want to spend 45 seconds loading the application only to spend a couple minutes with it, which is why Ajax is a good fit here. No loading. It also doesn't try to push Ajax to far, it uses very basic techniques, which is one of the reasons it is popular.
What it comes down to is that when building web applications, or looking at building Rich Internet Applications, use the right tool for the job. Sometimes that will be Flex, or it may be WPF down the road, or Apollo. But every once in a while, it's going to be Ajax, just like Joe's Goals.