2 Answers

Best info I could find.

USA

The United States of America is generally very strict with criminal records, no matter how minor or how long ago it has been. They do not have any concept of "spent" or "pardoned" convictions, meaning you must truthfully answer any questions about criminal convictions, even if your convictions have been spent or pardoned in your country. If you are a citizen of a country that participates in the Visa Waiver Program (VWP), any convictions, unadjudicated arrests, or even a previously refused visa makes you ineligible to travel on the VWP.

There are numerous crimes that makes you ineligible to enter the US, including "crimes involving moral turpitude." Moral turpitude is a legal concept in the United States for which the definition can seem imprecise and the list of offenses, which can vary somewhat by jurisdiction, can include everything from shoplifting to murder.

If you are convicted of a crime involving moral turpitude, you are ineligible to enter the US and little relief exists for this, except in cases deemed to be "purely political offenses" which can be open to interpretation by the immigration officer.

Being convicted of an "aggravated felony" is even worse, though just like crimes involving moral turpitude, these also have a very loose definition, therefore the offenses can change over time. However, there is absolutely no relief, and anyone deported or excluded for this reason cannot ever enter the US.

Attempting to enter the US after having been previously deported without a proper visa is a serious felony under US law, and is punishable by up to than 20 years in prison. The US conducts extensive security checks on all visa applicants.

http://wikitravel.org/en/Traveling_with_a_criminal_history

If you mean USA--  if they have committed a felony and was deported, I would hope they do not let them back in.   You say North America, you mean USA or Canada??