It's difficult to come up with hard and fast rules on when to Ajax-ify an app. In general most web apps/sites can benefit from at least a little more Ajax;-)
Sites like news, blogs, home pages and other text content heavy sites should be very cautious about using Ajax. There are many risks related to SE0, linking, accessibility and just plain annoying users that you need to consider.
Data centric web apps like ecommerce sites, CRM, accounting tools, social networking, email clients, workflow tools will generally benefit from heavier use of Ajax. But when proper usability and interaction design skills are applied.
In Enterprise Ajax we cover many of these issues in the latter half of the book. The case studies in the last chapter will likely be of of particular interest to see how other companies have benefited. The usability chapter points out a couple common pitfalls that show where you can go wrong with Ajax.
Enjoy