A criminal record can follow you long after a sentence has been served. Anyone with even a minor criminal past may have problems embarking on international travel. However, Mexico is relatively relaxed regarding entry requirements for those with criminal records, especially compared to its northern neighbour, the United States.
Mexico's entry requirements for foreign citizens are unspecific about individuals with a criminal record entering the country. For most minor criminal offences, individuals are not specifically barred from entering Mexico. Those with outstanding warrants are unlikely to be allowed entry, and individuals on probation or parole are likely to have problems. The nature and history of the criminal record in question determines ease of entry into Mexico.
Circumstances will dictate your ability to travel to Mexico. Before leaving home, check with the Mexican embassy or consulate in your home country to determine whether your criminal record will be problematic. American citizens with a felony record might be denied entry to Mexico. Certainly, those convicted felons who are still under supervision in the U.S.--whether it's probation or parole--are unlikely to be either allowed out of the U.S. or into Mexico. It's possible to apply to have a criminal record expunged for travel purposes, depending on the crime. In the past, individuals on the "No-Fly List" compiled by U.S. authorities have been denied entry into Mexico. The Canadian government, having conferred with the Mexican authorities, warns that Canadian citizens with a criminal record may be refused entry into Mexico and may have to return home on the next available flight.
For nationals of a country other than the U.S. or Mexico, transit through the U.S. on the way to Mexico is not advised. For example, Canadian citizens with criminal records may be allowed to travel directly from Canada to Mexico and gain entry without problems. However, those same individuals are likely to be refused admission into the U.S. due to a criminal record, so a flight from Canada to Mexico with a connection in the U.S. might end with an immediate return trip to Canada. U.S. immigration services do offer a travel waiver for certain foreign nationals with criminal records.