A connectionless service is one in which there is no long term connection between consumers and producers as multiple messages are passed back and forth. Connectionless services can be either stateful or stateless.

Web services are built as connectionless services in order to improve scalability over connection-oriented services. A connectionless service can behave like a connected service by building it as a stateful service.

One thing to point out, though, is that connected vs. connectionless is a concept that can vary depending on what level you're observing. SOAP messages being sent over HTTP are connectionless to the programmer. However, HTTP itself is a request and response sent back and forth over a short-lived connection using TCP, a connection-oriented protocol. TCP in turn is implemented on a connectionless protocol: IP.