Any significant reasons not to use AJAX?

It depends on how you plan to use it, IMO.

1) If the site will absolutely fail without it, you are excluding users with scripting disabled. I think it is fair in many scenarios to limit but not remove functionality for no-script users (for example, Google doesn't autocomplete searches if you have scripting disabled; it can't...but the basic search still works).

2) The right techniques need to be used in the right place. For example, an ASP.Net UpdatePanel will perform horribly if you dump thousands of elements into it.

3) I am becoming a bigger and bigger fan of content that is loaded in small blocks on the page that does not require a full refresh NOR does it require the whole page to be executed again. This lends itself to a SOA nicely, but is even more subject to the limits of #1.

4) EDIT: Don't create UI elements that (due to AJAX) behave unexpectedly. For example, I once built a dropdown list that only populated when it was toggled. Because of latency and DOM creation time, it wasn't responsive. Furthermore, the size would often change based on what elements were dynamically added. You could propose ways around these problems, but that was still an incorrect use of the technology.

AJAX is a tool for a job. If your application is best served by the tool, use it.

Edit -- just make sure the tradeoffs are well understood. Also, nothing in using AJAX prevents you from having a non-ajax backup ready for if you need it...

Obviously, there are many popular sites that rely on AJAX, so it certainly need not be avoided if used well. However, there are things to consider:

• Will users need to be able to deep-link (i.e. save bookmarks to "pages" that have been created dynamically)? Will they need to use the back button to navigate? (Both of these things can be done using AJAX but they need to be explicitly considered, as naive implementations of AJAX can make them work poorly or not at all.)
• Will the use of AJAX have a negative impact for disabled users (e.g. those using a screen reader)?