Of course there should be a statute of limitations. Why should somebody be accused of a crime out of the blue 20 years later and have to try to reconstruct their life and track down witnesses after all that time has passed. The defendant would be at an extreme disadvantage over the evidence and witnesses. That and a speedy trial are some of the reasons why we fought a revolution.
There is no statute for murder or manslaughter, for most other offenses the statute is two years. However, some sex offenses, robbery, burglary, arson forgery and perjury have a five year statute. For frauds, the statute is extended until one year after the fraud is discovered. There is a very short statute for most traffic summary offenses. However, the two year period does not run, while the defendant is absent from the state or while he reasonably cannot be found. So a game violator from Indiana who commits a violation in PA and leaves the state, can be charged whenever he may return to PA, even decades later.
A person who has no known address or place of employment, can be prosecuted when they "resurface" There are such individuals who have no driver's license, no fixed address and move around so much that they can't be found.