I was just reading an article entitled "Stop Using Ajax!" on Opera's Dev site (Link: http://dev.opera.com/articles/view/stop-using-ajax/). The author's premise comes down to this: Ajax does not play well with screenreaders and other such accessibility devices and, since you don't need it anyway, don't use it! Yes, that glosses a few things over. He also says that Ajax is simply not mature and that, some day in the future, it will hopefully be mature enough to be accessible.
The argument really all comes down to accessibility. Yes, he mentions usability, but he does so only briefly with the majority of the argument focusing on accessibility. The reason is simple: Ajax is a godsend for usability. It allows things to feel faster by not reloading the page (and, of course, perception is 9/10 of the game for end user applications) and allows for usage paradigms that are more like those found in desktop applications (which are more familiar). Finally, it makes the whole process of whatever you're doing less ponderous if you can simply work on one page rather than clicking through a chain of them.
As for accessibility, I certainly see the issue. Screenreaders really do not handle Ajax applications. They are, by and large, stuck in 1996. Though, even here, the argument has some flaws. He uses the photo-sharing site Flickr as his example of improving by not using Ajax. However, this example is specious as Flickr is one of the sites least likely to benefit from increased accessibility. If your vision is impaired (or absent) to the point of needing a screenreader, how likely is it that you will be able to look at photographs? Finally, harping on Ajax for this point is kind of ridiculous. Ajax works well for just about everything but automated tools like spiders and screenreaders. The correct conclusion would be to make a call on those who write these tools to work better with the web of 2009 rather than impairing the usability of the web for the 90+% of people who are actually glad to see web technologies improve. Furthermore, if we revert back to using older technologies, we then do not have people pushing the envelope and there is yet less reason for Ajax to "mature".