You can do this best using Firebug for Firefox :)
When you open firebug, open the net panel and you can see all traffic the browser's dealing with. If you want just the AJAX requests, there's a bar under the main tabs, select XHR.
There's more info available on the net section of the firebug site.
If I misunderstood the question and you want to see all javascript activity, then Firebug does this as well, just open the Console panel and click profile, this will let you see what's happening on the client with all javascript.
As an aside, if you need an IE specific tool, I'd really recommend dynaTrace AJAX Edition (also free!). It's a very in-depth profiler specifically tailored for IE.