You can use any medium you like for these connections. It depends on the interfaces available on each of these devices. Obviously they need to match at each end of the cable, but you can get fibre and copper (RJ45) cards for PCs and Servers, as you can for switches and routers.
There are many different types of connectors and different media types that can be used. See this SearchDataCenter tutorial for examples. As previously mentioned, RJ45 is a typical computer connector type and goes on an 8 (4-pair) solid copper cable. Other media would include fiber and can also be used to connect computers, switches and routers.