Salve Kaeso,
Interesting question.
I'm certain that there was crime in Rome(every major city has trouble with that) and I can imagine that there were certain districts in Rome that you wouldn't want to be at night.
An example of crime that surely would have to have been organized was smuggling. Pirates were also well known and I can already imageine that bribery was frequently used too.
However, I don't know if there was something like a Roman maffia or yakuza.
Vale bene,