Dengue (or, according to Webster 1913 in an uncharacteristically chatty moment, breakbone fever) is a nasty tropical fever that is transmitted to, and between, humans by mosquitoes - mosquito vectors, they're called in epidemiological parlance. The mosquitoes that carry dengue are day-biters, not night-biters like the ones that spread malaria. There are several distinct but related viruses that cause dengue, and recovery from one gives a lifelong immunity to that strain, but not the others. Dengue was considered to be non-fatal until the 1950s, when dengue haemorrhagic fever (DHF), a potentially lethal complication, was recognized. DHF is a leading cause of childhood mortality in some Asian countries. Dengue was once prevalent only in Southeast Asia, but as the mosquito vectors have spread, so has the disease. It's now common throughout Asia, Africa, and South America, and have even been reported in the southern United States. The mosquito is an urban one, and dengue outbreaks in poor "third world" urban slums can be particularly deadly for young children.
Dengue is a flu-like illness that lasts, typically, from three days to about a week. Classic symptoms are an abrupt high fever, severe headache, a rash, pain behind the eyes, and arthritis-like muscle and joint pains (hence breakbone fever), although children rarely exhibit more than a rash. Conversely, children are at much greater risk of death from DHF, which is characterized by vomiting, coughing, abdominal pain, internal haemorrhaging, and, in severe cases, circulatory collapse and death. For classic dengue, the best treatment is just to ride it out: bed rest, lots of fluids, perhaps aspirin for the aches and pains. I've had dengue, and though it was exhausting and unpleasant, it was manageable. DHF, naturally, requires more aggressive medical treatment: get thee to the hospital if you've got this!
Research is being done on a vaccination for dengue, though the task is complicated by the fact that four viruses are involved. The best preventive measure at the moment is killing the mosquitoes by eliminating standing water, which sounds reasonable unless you live in a slum where water supplies are intermittent at best and where you must store what water you can when you can get it. In cities like Bangkok, many slums are built on stilts over swamps, making them a perfect breeding ground for mosquitoes. The Thai government has instituted a number of measures, from DDT in the fifties to larvae suffocating agents now, to control the mosquitoes which make dengue and malaria endemic there. But I got dengue when I was in Thailand - on an island, not in Bangkok - so I'm living proof that these efforts haven't been completely successful.
The World Health Organization's fact sheet on dengue, which has been helpful to me in writing this node, can be found at
http://www.who.int/inf-fs/en/fact117.html
There's also some interesting hypotheses on the mosquitoes in question and how they evolved, as well as scientific details on dengue, at
http://www.biohaven.com/dengue.htm