XML-RPC is an standards-based protocol that can be considered the predecessor of SOAP.
Like SOAP, it is based on XML, but its definition is a lot simpler, resulting in a cleaner message format and less risk of differences and incompatibilities than SOAP.
You would use XML-RPC in scenarios where you need to communicate with existing XML-RPC services, or when communicating with platforms not directly supported by the Remoting SDK that do provide an XML-RPC implementation - such as Java or PHP.
You might also use XML-RPC when you need a simple human-readable messaging format - for example for debugging or monitoring purposes. In this case, you might also want to consider PostMessage.