The most common health problem experienced by travelers to the Virgin Islands [1] is sunburn. Nevertheless, the possibility exists for more serious problems, especially if you take risks swimming, diving, boating, driving, or with sexual behavior. Health care in the islands is generally good, although specialist services are limited, and ambulance service may be very slow, especially in remote or outer islands.
The U.S. Centers for Disease Control (877/FYI-TRIP, www.cdc.gov [2]) maintains up-to-date health information for travel destinations around the world, including the Virgin Islands. This is a good resource for travelers.
Before traveling make sure you are up to date on all routine immunizations, including hepatitis A and B, tetanus, diphtheria, and measles. There is no risk of malaria or yellow fever in the Virgin Islands.
Links:
[1] http://www.moon.com/destinations/virgin-islands/discover-the-virgin-islands
[2] http://www.cdc.gov