For the web site I\'m building (targeted at mobile users) I\'m thinking of using some Ajax controls. I\'d like to know which mobile browsers do and don\'t support Javascrip
Given "recent" phones, you'l find the answer is "most of them".
Along with the sites already listed, consider Device Atlas.
You could use something like WURFL to find the capabilities of the mobile devices serverside and present a page accordingly.
This may be slightly OT, but it's worth noting here, w.r.t. direct javascript support, that there's two types of mobile "browsers" - there are browsers with JS interpreters in them (like Opera Mobile, iPhone Safari, Droid) and then there are "thin clients" (like Opera Mini, Bolt, Skyfire etc.).
Thin clients support scripting, but do so in a different way. They have no JS engine on the phone - the JS is executed on the server and the result of that is then sent to the browser.
I've found ppk's list on quirksmode very helpful. It's not a 100% complete resource, but should cover most major browsers.
The default browsers included in Android, iOS Safari (iPhone) and Nokia all support JavaScript and Ajax. As does Opera Mini. Be aware, though, that it can be disabled (at least, in Opera Mini and Safari).
Quirksmode has compatibility tables for mobile browsers. When in doubt, use feature detection and try and leave a fallback for when JavaScript is disabled.