As a practical matter, I'd say that the vast majority -- probably 95% or more -- of those going just to Ambergris Caye or to other cayes don't get any shots or take any other medical precautions. Inland, except around Belize City, the CDC does recommend malaria prophylaxsis (chloroquine) though again many visitors don't take anything.
U.S. and other expats living in Belize rarely take any malaria prophylaxsis.
Personally, I think it's always a good idea to have your basic sticks (tetanus, DPT, Hep A and perhaps B) up to date, whether you're traveling to Borneo or Boston or Belize. If traveling in more remote areas of Belize, especially in the far south or near the Guatemala border, chloroquine is a safe, cheap insurance against an unlikely chance of malaria. It's also a good idea to protect yourself against denque and other mosquito borne diseases by using DEET (malaria and dengue, however, are carried by two different kinds of mosquitos and they are active at different times of the day.)
You can check with your doc, tropical medicine specialist or the CDC for advice, which naturally tends to be on conservative side.
Belize First Magazine http://www.turq.com/belize