How to separate the display and peripherals from the actual computer?

I am trying to see if its possible to toss all the computers in the server room and just run cables out of it.

The end goal is you just sit down at your desk and all you have is a display and peripherals. No computer can be seen or heard.

One idea is just to pass the required cables through the wall of the server room and setup the display and peripherals on the other side. But how do you do it in such a way you don't get all the server room noise? The required cables are different for every user, you can't just pass exactly what you need and seal it all up.

Another idea is just to use Ethernet for everything. You can get DVI/audio/USB over Ethernet. But then that's super expensive.

EDIT

And these computers will be used for more than just email. They will be powerful and noisy machines.

EDIT 2

My goal here is to reduce noise, reduce cleaning (of dust off computers), reduce cooling by centralizing and removing computer cases, save space, and increase security.

Solution 1:

For one-to-one I would get KVM extenders like the ones from Belkin.

For many-to-one I would get KVM switches from Avocent.

Solution 2:

The answer really depends what you are looking to do.

If you are looking to take existing systems and move them into a separate room, that is straight-forward, although likely hard to execute. You buy devices like this which convert KVM cables to Cat5, and patch the desk location to the computer location. The difficulty is more in where you put the computers and how you manage the cooling, power and wire. This will not scale well.
NOTE: if physical security is the concern, it might be easier to use a locking box (like this) for the CPU units.

If you are looking to update the infrastructure, there are two approachs.

One is "desktop virtualization" (aka terminal services). Basically you put a small number of servers up, setup terminal services (or Citrix MetaFrame) on the servers, and deploy thin clients at each desk. The thin client only runs the program to connect to the terminal server, and the terminal server runs all of the desktop applications.
NOTE: PanoLogic has a very interesting desktop virtualization solution.

The second is to implement a "Blade PC" or "Centralized Desktop" solution (like ClearCube) where you install specialized computers and hardware in the data center, and special connector boxes at the desktop. Conceptually similar to the "use your own PC" method, but it scales well, works well, but is somewhat costly.

I hope this helps.