Yes. All it takes is two computers connected by an ethernet cable. Whichever of the two is providing a service to the other is deemed the server. Whichever of the two is using the service provided by the other is deemed the client. It's as simple as that.
Of course you can expand that into one client accessing MANY servers, or MANY clients accessing MANY servers w/ the help of a local, switched network. And if those servers existed on the Internet, then you’d need a router in order to navigate outside the confines of your local, switched network to access them.