At the moment, the only fully supported language, and the de-facto standard for DOM tree manipulation in the browser is JavaScript. It looks like it has deep design issues t
If you're willing to restrict your customers/visitors to specific browsers, and possibly willing to require them to install a plug-in, you could look at MS Silverlight -- a readable overview is on wikipedia. With Silverlight 2, you can run, client-side, code you've written in C#, IronPython, IronRuby, VB.NET, etc; the free Moonlight clone of Silverlight, from the Mono project, promises to bring the same functionality to Linux.
In practice, most developers of web apps and sites prefer to reach wider audiences than Silverlight (and eventually Moonlight) can currently deliver -- which means sticking with Javascript, or possibly Flash (which uses a similar programming language, Actionscript).
So, gaining substantial mindshare, adoption and traction for anything else is proving to be an uphill fight even for Microsoft with its large groups of engineers and marketing budgets and a free-software project on the side (to possibly ease worries about proprietary lock-in) -- which may help explain why there's very little interest, e.g. on the part of the Mozilla Foundation, in pushing towards such a goal. "Apart from interoperability", you say: but clearly the issue of interoperability is THE biggie here, given what we observe wrt Silverlight's progress...