There is an increasing paranoia about "safety and security" nowadays. As people become more and more urbanized, more and more affluent, and more and more insulated (which I think is a consequence of the other two factors!), there is more and more worry about "safety and security". This worry manifests itself in many ways. People are unwilling to let their children step out alone or even exit the "complex" where they stay even to go to a grocery shop a few hundred meters away; teenage daughters are advised not to travel anywhere unless in company; and whole communities cocoon themselves inside the claustrophobic confines of a gated community. There is an increasing reluctance to meet the "other" world that lies outside the comfortable confines of what we are accustomed to; our houses are insulated, our cars are a refuge from the world; and our offices are an escape from even knowing what the weather is outside. I am sure a lifestyle like this that insulates us on a daily basis from everyday reality contributes in a big way to our paranoia on "safety and security".
The other factor is of course, the media. Anything dramatic and full of human interest is what it wants to play up on, and rapes and assaults are as dramatic as they get. Reading such reports being hyped up in the media induces in us a state of mind of being constantly under assault, and we go around fearing for our lives as a consequence. If there were no newspapers and TV, would we not be feeling safer about the world? News, especially the way it is served up nowadays, more often than not fuels needless anxiety.
In general, I feel it is generally very safe anywhere in India. All you need to do is drop your defences, be genuine, and soak in the companionship of the people around you, wherever you are, and there is no need to feel unsafe.
This whole thing about safety and security is a bit over-hyped. I have never felt unsafe in my life - I think it is more a state of mind than a state of actual physical reality. If you have nothing worth stealing on you or in your home, if most of your assets are either immovable or locked up in a vault somewhere, or even better, securely dematted (meaning, it doesn't even exist :-) ), there is nothing to fear from the robbery angle. In fact, I sometimes forget to lock my main door at night, and during the day, when the whole family is out, we leave it merely shut, not locked; for the hassle of everyone carrying keys is a bit too much. We have full-time live-in maids for the last twenty years; their average tenure is two to three years, and never once have we carried out a police verification or any kind of verification before hiring them. Since there is nothing to rob at home, what is there to worry?
As to physical safety, that danger is always there, isn't it? That you will be accosted somewhere and beaten over the head, or maybe sexually assaulted or "eve teased' in case of women. The probability of getting hit by a car when you are crossing the road is far far higher than that. Does that stop you from crossing roads? Can't stop living life fearing the extreme consequences of a low-probability event.
Paradoxically, I feel that the more you fear such an event, the more the chances are of something like that happening to you. Trust the world, step out, and nothing is going to happen. By not doing that, may be we are missing out on so many other experiences, that it is not worth holding back. May be what I say works only for India and not for some parts of the world; may be some people here may disagree with what I say even with reference to India; may be I am being dumb by not recognising the "dangers" out there. But I have lived by this philosophy of not ever worrying about safety or security, and have generally been happier for it.
I will make an exception for Delhi of course. I would not advise any woman to travel alone in Delhi after dusk! :-)