And from another site:
Cockroaches often are a health threat.
In general, the habits and high reproductive rate of pest cockroaches can lead to large populations which spread disease organisms, contaminate and eat our food, and cause allergies and even asthma.
Cockroaches have been reported to spread at least 33 kinds of bacteria, six kinds of parasitic worms, and at least seven other kinds of human pathogens. They can pick up germs on the spines of their legs and bodies as they crawl through decaying matter or sewage and then carry these into food or onto food surfaces. Germs that cockroaches eat from decaying matter or sewage are protected while in their bodies and may remain infective for several weeks longer than if they had been exposed to cleaning agents, rinse water, or just sunlight and air.
Good sanitation and habitat reduction, along with vacuuming, surveillance, a baiting program, and some sealing of cracks can usually quickly reduce or eliminate a cockroach population. A trained, certified Pest Management Professional (PMP) has the knowledge and tools to evaluate the situation, guide and advise on sanitation improvements, and accomplish the remaining steps.
Recent medical studies have shown that cockroach allergens cause lots of allergic reactions in inner city children. They were even shown to cause asthma in children. These allergens build up in deposits of droppings, secretions, cast skins, and dead bodies of roaches.
Adequate control of cockroaches is needed in such settings to help prevent the build-up of dangerous concentrations of their allergens. Where large cockroach populations are already well established, and in older buildings, or in buildings which allow roaches to easily move between rooms or apartments,
very good sanitation by one occupant will not solve the problem. In those cases, the help of a trained, experienced, licensed pest management professional will probably be needed to reduce the problem, and effectively work toward eliminating the roaches.
http://www.pestworld.org/Database/Article.asp?ArticleID=16&UserType=Consumers