Depends mostly on the web server and web language you run on Linux more than anything else.
If you're using Apache Tomcat, look at Axis2 (http://ws.apache.org/axis2/) and CXF (formerly XFire at http://cxf.apache.org/)
JBoss has web service support built-in (JBossWS) so it's fairly easy to use and since it's a Java EE server, it uses standard web service code that is portable.
You can also write web services using PHP if you use that on your web server.
Apache = IIS
PHP or Java EE or JSP or JSF = ASP.Net
There are a lot more choices in Linux land...
