There is no camping on Ambergris Caye, unless you make arrangements with a private property owner. I believe Vega's still offers camping on Caye Caulker, though for about the same money you can stay in a budget hotel.
Someone else mentioned Glover's Atoll Resort, and that does have cheap (around Us$100 a week) primitive camping.
There also is camping at Half Moon Caye, a national marine reserve, and at various small remote islands off the central and southern part of the country, where in some cases you need to get an okay from the caretaker on the island, if there is one. Getting to these islands is the problem, however -- it's expensive, as you have to hire a boat.
On the mainland, the place with the most camping opportunities is Cayo, where there are three or four small campgrounds plus several hotels (Trek Stop, Caesar's, Clarissa Falls and others) allow camping on their property. There also are camping opportunities in Corozal Town, at a few hotels in Hopkins/Sittee Point (e.g. Tipple Tree Beya Inn), at Cockscomb Preserve. There were a couple of small camping areas at the north end of Placencia village, though I'm not sure what their status is now. Placencia is still pretty beaten up from the hurricane in October.
--Lan Sluder www.belizefirst.com