We have a web site that needs to display address information that is stored in Exchange.
We plan to get this information by calling Exchange web services.
Question is what are the rights required by the user that will call the web service?
Is it possible to setup a user that has only read rights, but at the same time is able to connect to the web services?
The user you are connecting to Exchange web services with needs to have the rights to access the information in Exchange. I'm not sure what your trying to access, but for arguments sake let's assume it is a mailbox, then that user needs to have the rights to access that mailbox, if you only need read only access, then that is how they should be set up. This really has very little to do with the web app side of things, and much more to do with Exchange permissions.
The question then is how you access from your web application, is your app going to run as the user with those rights, or just impersonate that user when accessing Exchange.