Joe Hewitt, in this Dr Dobbs article talks about using the Firebug extensions to inspect and debug Ajax applications (or any browser-based JavaScript application). It also has CSS inspecting capabilities, editing JavaScript on the fly, inspecting HTTP request and responses, logging, breakpoint debugging and profiling. A useful howto.
Apart from being an elegant debugger, FireBug offers the developer hooks that can be used from JavaScript, offering logging, assertions, performance measuring, and command line functions for inspection or traversing a document.
All of the tools you need to poke, prod, and monitor your JavaScript, CSS, HTML and Ajax are brought together into one seamless experience, including a debugger, error console, command line, and a variety of fun inspectors.