Javascript language is predominantly used for Web development, on the client side only. There is a remote possibility to use what is called "Server-side Javascript".
See:
http://en.wikipedia.org/wiki/Server-side_JavaScript[
^],
http://en.wikipedia.org/wiki/Comparison_of_server-side_JavaScript_solutions[
^].
See also the Web references from these articles.
As far as I can see, Server-side Javascripts are quite exotic these days, as Javascript language, with all its flexibility, is a script language, not compilable one, it's hard to debug and on the server side it hardly can compete with modern powerful server-side technologies, such as ASP.NET or, say, Python, Ruby, etc. Even though I can imagine the use of Server-side Javascript in development of Web application, it's much harder to imagine what can you do with it for the development of the Web services which are not Web applications. However, such application do exist. Take a look at the first link I found:
http://net.tutsplus.com/tutorials/other/how-to-create-a-web-service-in-a-matter-of-minutes/[
^].
I'm sure you will be able to find some more:
http://lmgtfy.com/?q=%22server-side+javascript%22+%22Web+Service%22[
^].
—SA