Popular destinations include parts of Harlem and the Bronx in New York City, Mother Theresa's Calcutta, the favelas of Rio and Sao Paulo in Brazil and some of the so-called "black townships" of South Africa such as Soweto outside Johannesburg.
The question is, why are tourists doing this? Does it spring from a heart- felt desire to contribute to the welfare of the city's poorest inhabitants? Or do people just go along for the entertainment?
The favourite big idea of some travellers - that a city's slums represent its "essence" - is a selective travesty. Certainly the East End of London has qualities that the cultural hotch-potch of the West End does not. But this doesn't mean, of course, that visiting the East End is going to earn anyone the gratitude of the poor.
London Walks, a company specialising in tours of historic interest, conducts walks in areas such as Whitechapel and Brixton. "We go into areas like these because they are of historical interest, not because some people call them slums," says spokeswoman Mary Tucker. "We certainly don't take people on tours specifically to look at poor people."
Not everyone agrees. Fernando Carioca, who guides tourists around the favelas (shanty towns) of Rio de Janeiro, thinks tourists should see his slum-dwellers. "Forty per cent of the population of Rio live in favelas," he declares. "If you miss this you miss half the city. It's only by seeing favelas with your own eyes that you'll understand they aren't all about criminality. Normal people live there. Tourists should know about things like that."
And in New York City, where slums are supposed to be off-limits to tourists, Harlem Penny Sightseeing Tours has been showing tourists deprived areas of Harlem for 30 years. "Black people didn't used to like white people coming in here because we associated it with strangers taking our homes and jobs," says a spokeswoman. "But now it's more acceptable. Tourism brings money. There are lots of new shops and restaurants around here."
But was it gawping tourists who brought in the money? Traveller Sarah Johnstone, who visited Soweto on a coach tour during a trip to South Africa, says her main emotion was sheer embarrassment. "A lot of the people just went on the tour to be able to brag about it to their friends afterwards. There was one guy running round someone's dirty kitchen with a camcorder. It really did feel like voyeurism, rich people looking at poor people. And I felt hostility towards us on the part of the locals."
But tourists by the coach-load are never an edifying spectacle, even in Bond Street or Knightsbridge. No wonder the Sowetans didn't like them. What Sarah Johnstone's experience really shows is that most of us are voyeurs. In which case, why not be proud of it?
Guy Moberly, travel photographer, finds slums fascinating - as slums. "I don't care what slum-dwellers think of me," he argues. "There's much more local flavour in a slum. In Harlem, the noise, the rudeness and aggression are quintessentially New York. And in, say, the slums of Bombay there's an intensity of experience you won't get elsewhere, even in India. The smell of shit and sewage, the collapsing shops, the incredibly rough looking people. It's not nice, but seeing that was a much more powerful experience than seeing the Taj Mahal."