To add to what everyone has said, be very, very aware when there is any kind of distraction, even a pleasant one.
When we arrived in Paris on the Eurostar, we were going to take a cab to our apartment, but there was a lineup of about 40 people at the taxi stand, and there were no taxis in sight. So, we took the metro with our luggage, which made it very obvious we were tourists.
At one stop, a couple of men with musical instruments jumped in through the front door of our subway car and began playing music. Another man boarded at the second door of the car at the same time. He stood extremely close to my husband (who was also standing), almost touching him, even though the car wasn't so crowded that he needed to stand so close. This made me very suspicious, and I did not take my eyes off the man, making it very obvious that I was watching. Eventually, he left the car and so did the musicians.
My husband had most of his money and his passport in a moneybelt, anyhow, but I am convinced that this was a group of pickpockets working together, with some creating a distraction while the other one tried to pick people's pockets.
So be very alert, not just in crowds, but when anything unusual happens that might divert your attention.
We do find moneybelts uncomfortable, and we wear them only when we are travelling between locations on our trip. We use the cotton kind, because they tend to be more breathable and cooler, we've found. The rest of the time, I use a cross-body bag and my husband uses a travel wallet in a front pocket.