Envjs is a Javascript library that emulates a browser scripting environment in an external Javascript engine like Rhino (the preferred target at this time), SpiderMonkey or V8. It was originally developed by John Resig so that he could use jQuery in non-browser scripting tasks. He also pointed out its possible utility in server-side Javascript.
Claypool is a Javascript application framework built up from jQuery. It runs in a Java Servlet container (it ships with Jetty).
Jaxer is billed as "the world's first Ajax server". It is a web application framework that allows one to write Javascript on the server side. Script elements in web pages can be annotated with the attribute runat="server". It provides libraries for all of the usual server-side facilities like security, database access, file system access, running external processes, etc.