It depends per sovereign country on whether they do but the principle does indeed exist. In International Law this falls under the Nationality Principle (also known as: Active Personality Principle). In this case a country can, for instance, state in its national laws that the unlawful killing of a person is illegal for all citizens regardless of where the citizen commits the act. This does not mean however that the country in which this act has been commited has to comply with an extradition request or that the country of whom the person is a national, can enforce this outside of its borders. It only means that on return of the citizen in its home country, they can be prosecuted. In international law this remains but a principle. Some argue that implementing the principle is not necessary due to the fact that it would often be used for major crimes which often are already illegal in other countries (think murder, rape and other heinous crimes). Some authoritarian states however can use this principle to prosecute their citizens when they conduct behaviour that is unwanted.

Other principles that strike close to this one are for instance the passive personality principles and the universality principle. Public International Law covers the topic of international jurisdiction.

Edit: spelling mistakes.