Rome once had its own criminal organization called the "Banda Della Magliana". The widely popular series Romanza Criminale is based on the exploits of the gang, but I guess everything in the series should be taken with a grain of salt. They've been gone since the beginning of the 90s anyways and were never big or powerful enough to become a nationwide let alone internationally operating group.

Rome is a big city so there's bound to be some organized crime going on. From what I've read the Casalesi have a known presence and several suburbs have seen activity of a couple of Ndrangheta clans.
There's a lot more going on in Milan for that matter. Cosa Nostra, Ndrangheta, Camorra and SCU all have a presence in the suburbs outside of several foreign criminal organizations, which are mostly Balkan (Albanian, Serb-Montenegrin and Bulgarian) and Chinese in origin.