Saint-Petersburg is not more dangerous than any other big city in the USA or Europe. Beware of pick-pocketers in tourist areas, try not to show big sums of money or credit cards in public places and use common sense. When using public transport, especially metro, stay away from gipsy-looking groups of people who try to create a crowd around you and steal your wallet in the process.
Be careful crossing the streets – some drivers don’t stop at the traffic lights. If you travel in winter, mind the icicles on the roofs of old building ( there are lots of them in the central part of the city).
If you are lost, try to ask younger people of student age for help as they are more likely to speak English ( sadly enough the majority of people in Russia don’t). In any case the citizens are generally quite friendly and will try to help you. 🙂