There are, actually, quite a few exceptions to the maxim "Anyone of full age may sue or be sued." I am not a lawyer, so these examples may be a bit rough around the edges, but I think you'll get the main idea. Let's look at the most common examples:
- The Crown. From what I can understand, you cannot sue the monarch of a country for their private behavior (this may be different in certain constitutional monarchies, but I think it is a general rule.) In some countries you can sue the monarchy for the behavior of agents working for the monarchy, but not for the behaviors of those working specifically for the government (such as police officers.) In other countries you can't sue them at all.
- Judges cannot be sued for things they do while carrying out their duties. I believe prosecutors as well, though this doesn't cover them while doing their investigations, only while in court.
- Foreign diplomats and officials cannot be sued, extended in some cases to their families and employees.
- Corporations can be sued for the actions of the corporation, but the individuals in the corporation cannot be sued for their corporate actions. Their might be exception here in cases where the individual willingly violated the law in their capacity as corporate officer.
- Those suffering from "diseases of the mind" that are ruled not responsible for their actions.
- Enemy combatants.
- In most cases you cannot sue the federal government or the state government for the actions of its employees when carrying out their duties. There are exceptions to this, but it is not an easy row to hoe. Basically, you can't sue the government when one of its employees is doing his or her job.
This is just a partial list, but I think I covered the big ones.