Can you give an example of when it would be appropriate to use a web service as opposed to non-serviced .NET component
Web service is one of main component in Service Oriented Architecture. You could use web services when your clients and servers are running on different networks and also different platforms. This provides a loosely coupled system. And also if the client is behind the firewall it would be easy to use web service since it runs on port 80 (by default) instead of having some thing else in Service Oriented Architecture applications.

Can you give an example of when it would be appropriate to use a web service as opposed to non-serviced .NET component