Carry your handbag in front of you as well as over your shoulder. Take as few valuables as possible. Always keep your passport and money under lock and key within your room. Better yet, take it with you always. But beware, there are bold and brazen pickpockets.
Children can be good theives.
They are lovely, but watch out for the ones who are not with parents. I was so concerned about crime that I stayed home rather than go on the subway with a group to see Red Square at night. They all had a ball and were escorted by a young engineering student who wanted to practice his English. I was the loser on that night. Just use caution and good judgement.