Web Services accessed either through their Proxy Classes that are generated using the Web Services Description Language (WSDL) tool (Wsdl.exe), or through the addition of a Web reference, by default do not run under the credentials of the caller.
The Proxies thus generated, have a property called "Credentials" which can be used to send the security credentials of the current user for the Client Authentication. It can be used by creating an instance of a class that implements the Icredentials interface (e.g. NetworkCredential class).
The below snippet shows its usage.
//Put this statement before the call
proxyName.Credentials = System.Net.CredentialCache.DefaultCredentials
Note: Anonynmous Authentication should be turned off, and Windows Authentication is turned on for this to work. For a Windows App, this will be the Windows Credentials, and for the ASP.Net Apps it will be the Credentials of the Worker Process