It depends on the situation. If we are on a tour where the driver or tour operator stays with the bus, then I feel okay leaving "some" things there - obviously not money, ID, etc. I'll leave any souvenirs we had previously purchased.
On the beach, unless lockers are provided, we do as LisaP and take turns being the guard. One exception to this is on the private islands where we will let our guard down a little. Of course, on the private islands we don't bring credit cards or lots of cash so there really isn't much for anyone to steal.