While Perche is largely correct, Romans themselves still worry about pickpockets. Here is a recent article from Il Messaggero advising Italians to be careful on the subway.

http://www.ilmessaggero.it/roma/cron...ne-823516.html

The tl;dr version of the article says to keep money and documents in your side pockets, separated, learn to recognize and keep the thieves at a distance, to never use violence and to warn those around you to decrease the profitability of their "business".

One note on how dangerous they can be in the article is that they once robbed a military man in uniform!

[note that the article was taken from this web site https://riprendiamociroma.blogspot.i...-come.html?m=1 whose name translates to let's take back Rome]