I've worked in a few print shops over the last 16 years each of which had a slightly different way of saving files. I'm a graphic designer and also do pre-press so I worked first hand with these systems.
First, as many have mentioned, stop saving on a desktop. Create a shared network folder that resides on a server that is properly backed up off-site, into the cloud, etc.
Organization formats:
Scenario #1
I worked in one shop that had a "Pending Art" folder with sub folders by customers names. This was for holding files of jobs that were not yet an official order. Usually still in estimating. Once they became an order, I as the graphics person would grab it out of there and put it in the "In Progress" folder and add the 6 digit job number to the front of the folder name. So it was like: #####_CustName_BusCard.
Once a week or so, the graphics manager (myself in this case) would go through and move the jobs we knew were completed into a network folder called "archive". Here, all of the jobs were stored by number in the format above.
Scenario 2
At another shop, they had one network folder with folders for each customer. Within the customers folder would be folders for each type of project (i.e.- Letterhead, Bus Cards, Envelopes, etc). Within each of those would be the native art files, along with a single folder for art/logos and another for fonts. One advantage I found to this was the ability to quickly find all of the customers files in one spot instead of spread across various folders by job number. The BIG problem, though, was since we had multiple designers, people would not always delete the old file, or overwrite it for fear of wanting to save the old for reference. And so we'd have files like "Johns Bus Cards_New", "Johns Bus Cards_Latest"....see the problem! How does one know which is the latest other than an unreliable modification date?! Another BIG problem was that one designer might make a folder for "Rancho Community College" while another designer might not see that one and make a folder called "RCC" or yet another "RC College"...so we'd end up with 2 or 3 folders for the same customer without realizing it.
My solution
After working in both of these scenarios, I made a combination of the 2:
I really liked having all of the customer's files in one location, so I kept the customer names as the parent folders. (No "Pending", "In Progress" and "Archived"). We just told the reps to send us the file once the estimate was approved. We made a rule that the folders had to be the customers full name, spelled out to avoid the duplicates. Within the customer's folders, we put the order number at the beginning of each job just like in scenario 1. This eliminated the need for "New" or "Latest"...we just knew the highest number was the newest and they automatically sorted themselves. Additionally, we got rid of the sub folders for things like bus cards, letterhead, etc and just saved all of the native art files by number and had 1 folder for "graphics/logos" and one for "fonts. This made it very clean and organized.