The solution is:
1) Find out what the problem is in the existing system that people are working around by sharing problems, and
2) Address that problem in a way that removes the incentive to share passwords.
Well put. Should be modded up. (the rest directed to monkeedude)
I have been managing small networks for about 13 years, and your post is exactly the problem. A relative "n00b" thinks they can dictate the way users work by putting a network in place and telling users to do it a certain way.
Well, that doesn't fly. In any small network, you have to look at the work flow and figure out what information these users need in order to complete their tasks. If Bob and Suzie need to share files, for goodness sake, map them an X: drive to a server, give them rights, and move on. Do it however you choose, script-wise, but do it. Use Groups. Plan your resources. This is Network Admin 101. Above all, work with the users, don't just think you're going to slap them on the wrist when they don't do it "your way".
Have you introduced this problem to your manager? What do they say? If your responses belong to your manager, then your manager doesn't have a great deal of experience in the IT field either. I'm not attempting to bash your post, but your entire point of view regarding management of the network should really be re-assessed. Some small network admins get those kinds of ideas in their heads and never let it go. My suggestion to you: let it go. Work with management to establish network documentation: Best Practices, Internet Usage, and a Policy and Procedure manual (see HR for help. yes, they are two completely different things). Establishing documentation will help the users better understand what's going on, even if they don't become immediately savvy. Working with the users to figure out their issues with the computer system will be a learning experience for you, too. Be open-minded and leave any defensive attitude at the door, as someone is bound to say something that you will want to take personally. Get past this phase of the network growth and you will reap the benefits.