If you run your own dedicated server, you might also have clients or hosting customers who purchase services from you. If you host websites, you probably do not spend a great deal of time visiting each client’s site, but you may have some form of monitoring in place. This raises many questions. Is monitoring actually necessary? Should it be limited to security, or should it include Terms of Service violations?
Before you even consider the issue of monitoring, you need to make sure you have a clear Terms of Service agreement that new customers are required to accept. The terms are not designed to be restrictive and prevent clients from using their services to their full potential. They are designed to protect the server from harm and make sure the websites do not violate any laws.
For security, monitoring is not only acceptable, it is critical. It can help you prevent security problems before they happen and also help system administrators troubleshoot them after they occur. For other matters, the ethical ramifications usually depend on the extent of monitoring and the reason for it. For example, if users run applications that cause the server to slow down, monitoring software processes can help lead the system administrator to the problem. For legal matters, there is really no way to monitor a site in violation short of actually visiting each site.
What you should keep in mind is that, as the owner of a private enterprise, you have the right to determine what can and cannot be done with your servers. As long as monitoring software is not intrusive and does not impede user accounts, there should be no problem.