There's no reason for paranoia in Cape Town, but there are a few things to look out for. Aside from busy nightlife zones like Long Street, avoid the City Bowl at night and on Saturday afternoons and Sundays, when it's very quiet. Street kids and roving teens are blamed for much of the petty crime, but sophisticated crime syndicates are often involved, and many of Cape Town's fraudsters are smartly dressed. Cell phones can be snatched from car seats through open windows and even out of people's hands while in use. Watch your pockets at busy transportation interchanges and on trains. Pick a crowded car; if you suddenly find yourself alone, move to another one. Public transportation collapses after dark. Unless you're at the Waterfront or are in a large group, use metered taxis. Better still, rent a car, but don't leave valuables visible and don't park in isolated areas. Despite thousands of safe visits every year, Table Mountain, which couldn't look less threatening, has been the location of several knife-point robberies in daylight. The point is, never be completely off guard.
Poor signage is an issue in Cape Town, especially in the black townships, where most streets still have numbers rather than names and many streets are not signed at all. Carry a good map, and visit township attractions only as part of an organized tour with a reputable operator. Women and couples are strongly advised not to walk in isolated places after dark. If you want to walk somewhere in the evening, make sure you do so in a large group, stay vigilant at all times, and keep flashy jewelry and expensive cameras hidden, or better yet, at the hotel.
As in other major cities, drug use is a problem in Cape Town. IV-drug use carries a high risk of HIV transmission, as does the sex trade (which also carries the risk of other sexually transmitted diseases). AIDS is a huge problem in South Africa, so exercise appropriate caution. The drug of choice for children on the street is glue, and increasingly "tic" or methamphetamine. You will undoubtedly come across many people begging in Cape Town, including kids. Please do not give cash directly to children, as this often supports either a glue habit or adults lurking in the background. If you are concerned and wish to contribute, consider supporting people who sell The Big Issue magazine (associated with a worthy organization of the same name) or giving food instead of money.