Are you including bandits and pirates? I can talk about that if so.

Did you have a specific group in mind? Like a group connected with finding slaves to fight in the gladiator matches, or the Christian sects, who were all outlawed by the Roman government for a long time?

I believe this will answer your question http://www.reddit.com/r/AskHistorians/comments/2npi1s/did_street_gangs_exist_in_ancient_rome/

Plutarch wrote a bit about the Cilician Pirates who were very powerful in the Mediterranean for several hundred years. Do pirates fit your definition of organized crime?

One the note of piracy, there seem to have been tribes on the Illyric coast who's very economic backbone was based on plundering and raiding.

Take the Adriatic Queen Teuta for example. When Roman Envoys came to her to demand an end of the attacks on Roman ships she told them that the customs of her people to allow any kind of gain made on sea.

It doesn't get more organized than that. However, as has already been pointed out, you may question if the raiding and plundering at this point should even be called piracy or organized crime, since this seems to imply that it was illegal. For the Ardiaei it cleary wasn't.

The Romans on the other hand certianly saw it this way. The refusal by Queen Teuta to punish her people lead to a war, which eventually left her people subdued and stipped from access to the sea.

If so, it almost certainly would have taken advantage of the trade routes. Considering the Roman Empire had an incredibly prosperous economy and great trade, if there was organized crime I doubt it was influential.

What about racketeering? I've read about it in historical fiction about Rome, but is there any evidence that this went on?