How dangerous is India for solo women travellers, or female-only groups?

Over the last few years I have traveled alone in touristed areas of Delhi, Kerala & Rajasthan. I am a 29 year old Caucasian woman. I have travelled alone extensively in Europe, North & Central America. I never felt unsafe, but I followed some basic rules.

Activities: I did not go out alone at night. I mostly didn't go out at night except in the absolutely most heavily touristed, backpacking westernized towns(Varkala, Jaisalmer). I took cabs & rickshaws alone, but avoided any that solicited me or where the driver had a buddy. On the bus or trains I would get asked many questions by the locals but no one was rude or unfriendly. Occasionally walking around I would get approached with 'do you have a boyfriend/husband? Do you want one?' type things, but it wasn't too bad. I have had similar experiences in Europe or USA although rarer. I felt safe walking around in the day, and on the long distance buses. I did not take the local buses. I didn't feel as safe in Delhi or Jaipur as I did in the smaller towns or cities.

Dress: I dressed conservatively for me: nothing tight or short. Nothing shorter than mid-shin, nothing showing the chest. I bought a couple of local scarves as soon as I could and wore those - fun shopping + a quick way to look more locally appropriate.

I went swimming in a normal one-piece suit in Varkala (very heavily Westernized) but covered up when I got back to my towel. There were people on the beach making sure no Indian men ogled the women too much.

There were many other travellers doing the same thing - more in Kerala than in the north, but in general it did not seem overly dangerous. You might get scammed, hard-sold, or something similar, but physical danger can be generally avoided.

Few points:

• While on the road, try to dress like Indian women. No, this does not mean that you have to wear a saree or a veil. Get a loose Kurta-Salwar (a long tunic that covers below the hips) stitched with a proper Duppata (shawl.) Use the Duppatta to cover your head, back and chest. Your attire should draw less attention towards yourself.

Kurta-Salwar:

Duppata:

A few days back, in a metro, I saw a western girl wearing a very transparent T-shirt. I could clearly see her black bra! Please remember that though India is a democratic country, showing off your skin (purposefully) and then complaining of eve teasing does not make sense here.
No, wearing low waist jeans which shows your lower back somewhat is NOT normal here. Cleavage showing is an absolute NO.

• If you have somewhat long hair, try to braid it. That's what traditional women do here.

• If male strangers try to talk to you like - "How are you doing?", "You are from which country?" etc.- do NOT respond, just give them a frown and look away. It is NOT normal for Indian women to respond to useless queries from male strangers.

• When in a shared auto, do NOT sit with the driver. Indian girls usually avoid going in shared autos until they get a proper back seat. Sitting with the driver in a shared auto is a complete NO.