If the wires are to an external drive or other hardware that is fixed, I like to use velcro straps as this is an easy way to keep wires tidy and also can be released when need be.
The wires for monitor , speakers and keyboard/mouse, and internet cables,
I make sure everything is in the positions that they will remain in and use holes next to my computer and monitor and modem. The holes are drilled just big enough for the wire connectors to fit through and I run them through the hole next to the computer and under desk and up next to monitor or modem or speakers.
For the mouse and keyboard I use a hole just in front of my monitor and run them through it so that they are able to be lengthened or shortened as needed as well.
The only exposed wires are right at the equipment that are being connected or about 12 inches of keyboard and mouse cable. Other than that, there is no exposed cables anywhere on my computer desk.