Having explicitly-stated policy helps prevent a lot of problems, and makes some problems easier to solve by delineating the responsibillities of users and system administrators.
From a system administrator's point of view, policy helps you know when and for what you have to monitor your system and its user activity. It also lets you know when you might have to intervene in cases of bad behavior, and what you have to do in those cases.
Most users will voluntarily comply with reasonable policies, and even if they don't follow the policy tend to protest less if they were made aware of prohibitions in advance. Good policy also provides a more stable and usable system for users.
While much of this discussion has talked about policy considerations that apply between you as a system administrator and your user community, it's also important to remember that your system and users work in a networked community that also has expectations of responsibility between its members. Some unwanted user activity or system malfunctions cause problems for your network neighbors and also need to be dealt with. Users may attempt to attack network security at other sites, stage denial-of-service attacks, spam, or harrass users on other systems; other sites will expect you to have policies to prevent abuse of their systems as well.
You will usually also be expected to protect the privacy of your users by not revealing personal information about them, even when they have violated system policies. Be careful to check the credentials of any law enforcement officers who request personal information; valid requests will have appropriate documentation and authorized law enforcement officials will honor requests for identification and documentation.