The good news is that violent crime against visitors to Delhi is rare. The bad news is that petty theft is fairly common, albeit no worse than in any other Asian metropolis. Pickpocketing and theft from hotel rooms are the most common complaints.
For tips on hotel security (for further details see Hotel Thefts). The risk of pickpocketing can be minimized by carrying all valuables in secured bags rather than loose in pockets, and by slinging bags over your neck and carrying them in front of you (backpacks are inherently less safe). Many travellers use money belts, although these are not necessarily secure. It is also a good idea (for women travellers especially) to exercise due caution after dark.