While staying in big cities of Russia, like in most other countries, one should be attentive in the streets, in metro, etc. The most common crime against travellers in Russia is pick-pocketing. In public places, especially in public transport, you should be careful and alert.
Be aware of pickpockets! Some pickpockets work in groups, so avoid people who are trying to sell just one thing to you, because at the same time somebody may be stealing your wallet. Do not keep your documents and your money in the backpack or in your back pocket. It is advisable to keep money in a money belt and make copies of the documents you have including your passport, plane tickets, visa and migration card. Mind your photo gear, expecially in St. Petersburg.
It is also important to be attentive on the streets because some drivers do not follow the traffic rules and may not let you cross the street. Use pedestrian crossings equipped with a traffic light or underground tunnels in order to cross a busy street.
It is not a good idea to walk alone late at night, especially in the districts out of the center. You are recommended to call a taxi to get to your place. It is better to call authorized taxi agencies. It can be expensive but it is much safer.