ASP.NET web services are the great way to expose your middle tier components via internet. These components offer no issue communicating across firewalls as they use SOAP as transport protocols that transmit structured data using HTTP channel. Thus, message can be easily exchanged through port 80, i.e. through internet data port without being getting hampered by corporate firewalls or proxy server.

Web services can fit in the situation when we require integrating disparate systems written by separate vendors via internet.

Web services are primarily being used for B2B integration like authorizing employees, supplier, electronically signing of invoice etc.