At work, we have three computers that we rarely use, but are essential and are always on. One is our server, one controls the voicemail system, and the third has to do with an accounting software that our finance department uses (I'm not sure what it does, though). At least once a month, we need to access these computers to perform maintenance, etc.

Right now, the station where these three computers are at is cluttered with tree of everything. Mice, keyboards, and monitors.

Is there a device that would allow us to attach all three computers to one set of a monitor, keyboard and mouse through some sort of switching box? I've seen devices that allow one computer to have multiple monitors, can we just reverse on of those?

Use a KVM switch.

Yes! That's exactly what I wanted! Bravo! And thanks!

You're welcome, Amazing Andrew.
Glad to be of help.

RealVNC if they are very far from your desk. Also KVM over IP, but that is an expensive option.