Well technically you can use it in a windows application....
The long way to implement AJAX in a windows application.
The short way to implement AJAX in a windows application.
Quite simply, don't. The biggest feature of Ajax is that it simulates many windows applicsations ability to provide data on demand with out any postbacks or whatever. You can tweak your windows application to go above and beyond what Ajax could do by researching multithreading and the WinForms API and learning how to stream data from its source and automatically propagate that to the UI with out causing a noticeable wait to the main ui thread. But thats more into data visualization & web 2.0 centric than AJAX in itself.