An application integration solution consists of several interrelated technologies. First you need an interface to each application involved so you can communicate with them. Then you need a messaging system that can deliver messages from one application to another application's interface. If the communicating applications do not agree on data formats you need some kind of translation technology. Finally, many application integration problems involve process management to ensure that each application correctly plays its role in the business process.
Web services afford you the opportunity to place standards-based interfaces on your applications. In fact, many commercial applications already come with Web services interfaces. Web services also offers standard messaging protocols that reduce the data transformation problem to translating one XML document into another. This is likely a much simpler task than translating one arbitrary data format intro another arbitrary data format. Standardized descriptions for business processes that interact with Web services have also been proposed and several vendors have already committed to adopting these interfaces.
Given all this, there is a high probability that Web services will one day become the standard application integration technology. Since many applications will have pre-defined Web service interfaces, purchasing proprietary adapters or commissioning custom interfaces will be unnecessary. Proprietary applications may still call for building an interface, but the Web services interface you build will be based on standards so you can use it with multiple vendors' integration products. What's more, proprietary messaging systems and process managers are no longer required, giving you the flexibility to shop for the most effective solution without as much worry about being locked in to a vendor.