Before we delve into whether federal crimes are subject to a statute of limitations lets define what the phrase statute of limitations means. Simply put, a statute of limitations defines a legally proscribed period of time that, if not fully elapsed, will allow for a legal proceeding to be initiated.
The main reason that the concept of statute of limitations has been enacted in criminal law is to prevent the accused from having to defend themselves against allegations based on evidence that is no longer retrievable or dependent on human memories which can be fickle and errant.
As a rule, when it comes to federal crimes there are no statute of limitations enforced on any crimes that are punishable by the death penalty. The same applies to certain federal crimes that are related to terrorism. Additionally, the same also applies to certain offenses that are of a sexual nature.
In most other federal offenses normally the statute of limitations by which most federal crimes must be prosecuted is five years from when the crime was committed. Exceptions exist for which the statute of limitations for certain crimes can be longer than the typical five years such as arson, theft of art and some crimes that are committed against financial institutions.
Typically the clock starts ticking on the statute of limitations immediately after the crime has been committed. However, when criminal conspiracy has been committed the statute of limitations starts running after the last affirmative act has been committed to further the overall scheme. The same applies to any offenses that have a similar continuance nature such as a number of possession crimes, as well as crimes that levy obligations on the perpetrators that they be promptly reported.
Source: Congressional Research Service, "Statute of Limitations in Federal Criminal Cases: An Overview," Charles Doyle, Summary page, Accessed June 15, 2015