Mosquitoes tend to come out at dusk and dawn. They are worst in urban and suburban areas where trash, flowerpots, cisterns, and other containers serve as breeding grounds. They are also common around ponds. Mosquitoes are worst in the rainy season and are easily tempered by breeze.
Bring insect repellent, especially if you will be camping or staying in rustic accommodations. Always keep screen doors closed. Mosquito coils, which are burned like incense, work well, but the fumes bother some people.
Another pesky bug is the biting midge, known locally as the sandfly. These annoying bugs live in sand and come out during dusk and dawn. They resemble a gnat and deliver uncomfortable bites. Bug repellent works against them. Be careful not to track too much sand into your room, villa, or boat, or sandflies will follow.
There are no dangerous wild animals or snakes in the Virgin Islands [1]. Many islands have large populations of feral cats and dogs, which can be problematic. Dog packs are known to attack livestock, especially at night. In the British Virgin Islands, look out for goats, cows, and chickens while driving.
Links:
[1] http://www.moon.com/destinations/virgin-islands/discover-the-virgin-islands