Thankfully I've never had a problem with pickpockets in Rome and I used to go there every few months for a couple of years or so (both business and leisure). I always keep my money in a front jeans pocket along with my wallet - would never put anything in a back pocket. Leave your passport and spare cash / cards at the hotel in a safe.
The real advice I would give you is to watch out around the Termini Railway station and major tourist attractions. Just be watchful but don't let it ruin your holiday.
The other critical advice is taxis. Don't take them unless they have been ordered for you by the hotel or someone you trust. Hailing a taxi at Termini or the airport is almost certainly going to get you ripped-off! Double, tripple or even more than the standard fare.
Regards
lme ff etc etc