Delhi has, unfortunately, a deserved reputation as being unsafe for women. Precautions include never walking around in lonely, deserted places, even during daylight hours, keeping an eye on your route so you don't get lost (download a map that you can use offline) and taking special care after dark – ensure you have a safe means of transport home with, for example, a reputable cab company or driver.
Taxi-wallahs at the airport and around tourist areas frequently act as touts for hotels, claiming that your hotel is full, poor value, dangerous, burnt down or closed, or that there are riots in Delhi. Any such story is a ruse to steer you to a hotel where they will get a commission. Insist on being taken to where you want to go – making a show of writing down the registration plate number, and phoning the autorickshaw/taxi helpline may help. Men who approach you at Connaught Place run similar scams to direct you to shops and tourist agents, often 'helpfully' informing you that wherever you're headed is closed.
Touts at New Delhi train station endeavour to steer travellers away from the legitimate International Tourist Bureau and into private travel agencies where they earn a commission. Touts often tell people that their tickets are invalid, there’s a problem with the trains, or say they're not allowed on the platform. They then 'assist' in booking expensive taxis or 3rd-class tickets passed off as something else. You're particularly vulnerable when arriving tired at night. As a rule of thumb: don’t believe anyone who approaches you trying to tell you anything at the train station, even if they're wearing a uniform or have an official-looking pass.
Many Delhi travel agencies claim to be tourist offices, even branding themselves with official-looking logos. There is only one India Tourism Delhi office; if you need a travel agent, ask for a list of recommended agents from them. Be wary of booking a multistop trip out of Delhi, particularly to Kashmir. Travellers are often hit for extra charges, or find out they've paid over the odds for the class of travel and accommodation.