I dislike cables. That Spaghetti mess of power chords, monitor leads, keyboard and mouse wires and so on that have lurked behind our computers for a couple of decades. Even after the onset of wireless peripherals some of these cables are absolutely essential and others are still preferred by some people. For most of us, there are ways to reduce your cable burden. There's one golden rule though:
Any solution you choose has to be at least as convenient as the one it replaces.
Sounds obvious. Get rid of your mouse wire and the unsightly cable is gone, freeing up desk space and preventing it from catching on your mug of coffee, right? Of course — but things are not that simple when you start talking about large-capacity external storage that you might need to access reliably and often. As said above, some cables cannot be eschewed at all. If in getting rid of your wires it proves to be more effort to use the new system than to just deal with the cables in the first place, then guess which one you're going to go with?
Your keyboard and mouse are the obvious place to start, but there are considerations here. If you're using a modern Mac then you're probably already wireless, and this has worked pretty well for me. With any wireless system there is the potential for signal interruption. I've had my mouse briefly lose connection once or twice in the last couple of years. In my experience the better quality the peripherals you have the more reliable and better range you will get. Logitech have been great in the past in my experience but Microsoft's own wireless mice and keyboards absolutely not so good. Particularly for gaming reliability is an issue, you may need to check out some reviews online and budget accordingly.
Storage is another place where you can ditch cables from your desk in favour of Network Attached Storage or even cloud storage such as Dropbox, Google Drive, OneDrive, or any number of similar remote storage services. If this network or remote storage isn't readily available at a moment's notice on your network, fast and reliable, then it's going to be frustrating. You also need to consider security — who else connected to your network might be able to see and browse through that storage, and how much effort will any security measures be to maintain? It's also important to consider the speed of data transfer across your wi-fi if you need to handle large files (would a Thunderbolt cable simply be better?), and if you really needed to for some reason could you take that storage with you as easily as a USB external hard drive?
Printers, scanners and the like have been wireless for a while. If you use iOS this is essentially a prerequisite of AirPrint. A wireless printer is much easier to find a suitable home for, and does not require exceptional network performance. I think this is likely the easiest place to cut the cord, especially if you'd like to get the printer off your desk altogether.
Where you have essential wires such as power cables, and you're as obsessive as I am, then you can do a pretty good job of hiding them. I use a dining table for a desk, and so it has panels on the underside of the table surface that I can tuck the Thunderbolt Display's wires behind using Bluelounge CableDrops (and I'm sure there are innumerable similar alternatives). The power cable runs hidden behind the panel, and is similarly affixed to the inside of the table's back leg. It's as out of sight as possible while still being connected. Similarly the power cable for the MacBook is mostly hidden. This has also stopped me accidentally catching trailing cables with my feet. Your desk may not have quite as convenient an obstruction but the principle will be the same.