MOST COMMON THEFT IS LADIES PURSE/HAND BAG SNACHERS. STRANGERS ON BIKES SNACH PURSES AND MOBILE PHONES ON THE COMMON STRECH OF THE WESTERN EXPRESS HIGHWAY RIGHT OUTSIDE THE AIRPORT. ALL TRAVELERS SHOULD BE ABSOLUTELY CAREFULL ABOUT THEIR HANDBAGS AND MOBILE PHONES. NOT SURE .. BUT GUESS THERE ARE PPL WHO FOLLOW RIGHT FROM THE AIRPORT AND SNACH PURSES/HANG BAGS/MOBILES ON THE WIDE HIGHWAY THAT CONNECTS THE AIRPORT.INCCIDENTS HAVE OCCURED FROM STRECH ON THE HIGHWAY MAJOR SPOTS BEING FLYOVER BRIGE RIGHT OUT SIDE THE AIRPORT, SANTACRUZ AND KANDIVALI.
During night it is very dangerous for lone travellers(especially women) to travel from the airport towards South Bombay especially till Mahim by taxis/autos. There has been several incidents of tourists being robbed of their valuables. Advisable to avoid leaving the airport during the night or better leave in groups. Organised gangs are said to be behind such crimes. One can dial the police control room by dailling 100(i guess it free, never tried it though)
The overwhelming majority of people you meet in your travels in India will not want to do you any physical harm. A few might want to part you from some of your money by overcharging or conning you. A few might be offensive, overly curious, or insensitive. Many will be extremely friendly, helpful, and well intentioned. In short, the people are probably a lot like those in your own country.
In India you do need to be careful of petty theft and minor scams but incidents of violence directed at travelers and snatch-and-grab crimes like purse or camera snatching are rare. (Gold chain snatching is frequently reported in urban papers, but this won't target foreign travelers. Indian women wearing the traditional marriage necklace are the victims)
What you are more likely to encounter, besides the inevitable auto rickshaw driver demanding a higher fare, are stealth crimes (a bag disappears on the train, a hand sneaks into a backpack) or some kind of scam (a friendly stranger offers to arrange a ticket and disappears with the money). You should maintain the same kind of awareness and watchfulness you employ in your own country. If a situation doesn't seem right, or you don't feel safe, take precautions. Be careful, but don't be paranoid.
Most times in India there will be a lot of people around. This can be sometimes annoying, but it also offers security. Passers-by will usually be quick to offer assistance if they sense you are having a problem. If you do encounter a threat in India it will most likely be in an isolated spot. Beaches at night are a classic problem area, especially near cities. They tend to be deserted except for bored young men from the city who may hang out there a recipe for trouble.