Since England had a habit of sending transgressors from jail to its colonies, there is a chance that you descend from someone who committed a crime, and there were any number of crimes, many of which would be considered minor today, that would have resulted in transportation.
The proceedings of the Old Bailey, one of London's central criminal courts, has posted 197,745 criminal trials on a website that is fully searchable. Even if your ancestor is from England or not, I would recommend this site for anyone interested in history. The BBC program Garrow's Law (I highly recommend that you buy the US DVD of series 1 here.) uses some of the criminal proceedings chronicled on the Old Bailey's website for inspiration.
A keyword search for my last name brought up an 1855 case where a witness (Richard Allen Sprigg) notes that his wife's maiden name was Atchley. My line has been in America since the early 18th century, so this is at best a distant relative. Using the surname field on advanced search only seems to bring up the main parties in the case, so I suggest doing another search with your surname in the keywords field as well.
I was also able to search by punishment, and there were 41,515 court cases which resulted in transportation.