The American continent was populated with criminals sent by England. Between 1615 and 1775 about 50,000 were sent mainly to Maryland and Virginia. They would be sentenced to servitude of anywhere from seven to fourteen years.
Colonial records and actually into the middle 1800s indicate that most criminals were not imprisoned but banished or punished. The punishment could include anything from branding to flogging or being placed in stocks. Some of these were very cruel methods, particularly being branded on the forehead with the letter of the offense. Sometimes offenders were sentenced to the ducking stool which, when placed near a stream or pond of water, would submerge them.
County court minutes will often contain information about the convicted and their offenses, most of which were non-incidental compared to today's social standards. These could include playing cards, gambling, swearing, not attending church, breaking the Sabbath, game-cock fighting or horse racing. People found quarreling or inciting a riot were also punished.
Your ancestor does not need to be a famous outlaw or criminal to be found in records. Reforms in the justice system brought changes, abandonment of the flogging, branding and other inhumane practices of earlier years. It also meant that prisoners were confined in jails and prisons and records were created.
If your subject was incarcerated for any length of time, he may show up on a decennial United States Census. Inmates in jails and prisons were enumerated and depending upon the information gleaned by the enumerator, you may learn about their offense. Common offenses were usually burglary, assault, battery and petty larceny.
This provides you with information to begin checking court minutes as well as newspapers. A good source for earlier newspapers is Genealogy Bank at GenealogyBank. If you do not have a subscription, check at your local library to see if it is available for patrons.
You can also check for your ancestor online at Blacksheep Ancestors, Black Sheep Ancestors. On this web site you can search for countries and topics. A search in the USA can be done by topics of Prisons and Convicts; Outlaw and Criminal Ancestors; Court Records; Executions and Insane Asylums. From any of these you will find many links to web pages with databases and information.
If you are researching in the United Kingdom, be sure to check The Old Bailey Proceedings Online at http://www.oldbaileyonline.org. They date from 1674 to 1913 and contain information on 210,000 criminal trails at the central criminal court in London. There is a lot of good reading here, even if you don't have English ancestry.
Some states have inmate lists online. The Colorado State Archives has the Colorado State Penitentiary Prisoner list for 1871-1973 at http://www.colorado.gov/dpa/doit/archives/pen/prison.html. This is an excellent web page which allows the reader to view not only the list but the history of the Colorado State Penitentiary, the types of records available at the Colorado State Archives and even a list of mug shots that are available.
The Connecticut State Library has the Newgate and Wethersfield Prison Records 1800-1903 that can be searched online at Newgate and Wethersfield Prison Commitments 1800-1903 (CT).
Curious about every prisoner to serve time on Alcatraz? Go to the web page, Alcatraz Prisoners.
Prison records that date before 1900 may still exist within the institution that created them and some may have been transferred to a different repository, such as a state historical society, local historical society or state library. A listing of federal and state agencies that may have records before 1900 can be found at http://maxpages.com/ourlostfamily/Prison_Records.
Should your research indicate that your subject was executed, you may want to begin checking the web page Before The Needles found at History of Executions In America. Be sure to read this thoroughly for statistical information and then search by area and state. Another interesting web page is Lynchings: The National Lists at http://www.geocities.com/Colosseum/Base/8507/NLists.htm.
Finding information on convicted relatives can be time consuming, but chances are with some Internet sleuthing and letter writing, you will obtain a good deal of information.