
When web pages become web applications. Then page reloads are history and you interact with your webapplicationin your browser in the page and with AJAX/AHAH you will get the data in and out of the page. Nothing new, that is what the marketeers label web 2.0.
But when users interact with pages without having to reload ... when pages become application .. this also means that traditional ways of measuring user activity that are hosted and used as a service, such as Google Analytics, will not be able to tell you what a user has done on a pageapplication.
There used to be a time when the success of a website was measured in "hits", way back in the nineties. Then -due to the fact webpages consisted of many HTML elements like Cascading Style Sheets- the success was measured in pageviews. For the last couple of years, the success is measured in unique visitors since advertisers are not that interested in serving the same ad for the 10th times to the same person. And now, due to AJAX, we have to find a new way of measuring the success of webapplication.
Yahoo! understands this and has been offering Yahoo! User Interface services for some time now for free that can be used by a webmaster to give a more rich feeling towards the user. This way, Yahoo still gets to see who is doing what on a website and can offer this as a Analytics competitor as well as use the data for having a better advertising offering with behavioral targeting. The downside is however that to make your pages application, you do more then some icing on the cake; User Interface gadgets are nice. But the real deal is in enriching your data for webapplication use, not just your user interface.

AJAX-As-A-Service (as a new way of Server Based Computing) suffers the same problems as the old way of doing Server based Computing like Citrix has; looking to the world through a straw. Local data and terminal screens from remote do not mix well; a document that is saved on a local harddisk and accessed via a terminal service application still need lots of bandwidth and leads to high latency. The same kind of poblems you encounter when you use hosted AJAX service that are not integrated with your site; the (meta)data of the user is on the webserver and the AJAX application is served from another webserver not able to access all rich metadata.

Therefor only websites that are based on a Content Management Systems that is old will use these kind of services, modern CMS-es like Drupal ship with their own plug-able extend-able AJAX library. And if that CMS enables you to turn a web-page into a webapplication, you have two options to have the right statistics based on the right data; logging from the CMS or raw logging from your website. Drupal never has been good in providing logging analyses; it is good for technical webmasters but the analyses is not usefull at all for marketeers and managers. Analysing raw logging yourself is IMHO still the best way; you also get to see those firefox users that block urchin or have the best firefox plugin aivalble installed. However, it takes time and most of the reporting is by far not as fancy as Google Analytics.
So we will see how AJAX will influence web-analytics, maybe CMS-es will provide better statistics?