Is it possible to have a client/server service that doesn't use sockets?

If they are both on the same machine, or have access to a reliable shared disk (although the processes that create and maintain that shared disk also use sockets, so I guess that one doesn't count) yes. Is it practical? No. Is it effecient? No. Does it make any kind of sense, what-so-ever? No.

How are they to communicate? Telepathically?