|If your printer has an Ethernet interface and you are connecting it directly to the computers Ethernet Interface then yes, you do need a crossover cable.|
However, a printer with an Ethernet Interface is supposed to be connected to a switch then every computer on the network will have access to it rather than go through another computer. Four port routers have a switch built in.
If you only have one computer and no network you would be better connecting via USB. Using Ethernet in those circumstances is an unnecessary complication.