I'm confident that you'll see a number of frameworks/libraries that can take advantage of JS running both client and server sdie in time for JSConf in April. The most public has been Yahoo's YUI team, with Dav Glass putting the effort into getting yui3 running in node.
Dav did a video presentation on yui3 in node:
http://www.yuiblog.com/blog/2010/09/29/video-glass-node/
IMO the most useful example/demo in the talk is screen scraping digg:
http://github.com/davglass/nodejs-yui3/blob/master/examples/...
He also provides examples of various yahoo widgets getting rendered as static html, which I think is also in that github repo, but I can't find his demo online.
I'm also working on putting a bunch of pieces together that would allow an app to be client/server agnostic but I've been "working on it" for months now in the background and I'm not finished so I'll just wait until I'm done to talk about it.
Writing good clean semantic HTML will help ensure that you need only write one HTML document that is then styled by one CSS document for the desktop and one for mobile devices. Plus writing semantic HTML will give you basic SEO for free.
I honestly wouldn't worry about the JS frameworks just yet unless you have something specific in mind that you want to build. There's so much other basic stuff to learn. I would tackle javascript after you have a good grasp of HTML and CSS.
But I can't imagine any cases where this is useful? Is it just the benefit that you don't have to think in two different languages or is there something more to it?