Traditionally I use FireBug to debug my AJAX requests. It lets you examine both the contents of your request as well as the response that was sent back from the server. (it also notifies you in the console when these occur, which is a useful feature that Chrome seems to lack).
In Chrome, I only seem to be able to view the requests, not the responses. When I try to examine the response the UI just displays "No Content Available" (Developer Tools > Resources > myRequest.php > Content). Do I have to turn something on to make the Chrome developer tools remember these requests?
EDIT: In case it matters, these requests are being made inside a Flash object.
If you are on a dev channel of Google Chrome:
http://www.chromium.org/getting-involved/dev-channel
...you should be able to right-click in the Developer Tools console, and click "Enable XMLHttpRequest logging".
Once it is enabled, you will see the XHR requests in the console, and will be able to click on them to take you to the resources panel, where you'll be able to see the content of an XHR.