Crime was a huge problem in London in the 1830s, when Dickens was writing, just as it is now. Novels and plays about crime were hugely popular. Some novelists wrote about crime because they had a particular point to make about the source of criminal behavior, or possible solutions to the crime wave. Other novelists wrote about crime just because they knew it would sell. Oliver Twist was hugely popular, but Dickens definitely had a point to make: he wanted to show how criminals really lived, in order to discourage poor people from turning to crime. He also wanted to show how external influences created criminal behavior as much or more than natural criminal urges.
In Oliver Twist, Dickens seems to be arguing that influence and environment, rather than inherent vice, cause criminal behavior; however, that position is undermined by several characters.
Criminality in Oliver Twist is not limited to the lower classes: characters like Monks and Mr. and Mrs. Bumble show all levels of Victorian society are equally culpable.