Deleting objects and different variables are usually possible, however delete actually does not delete objects in solidity but it sets the values to the default value, like 0. As in the following examples, setMyMapping creates a new mapping element and initializes with _value. However deleteMyMapping does not actually deletes that element, instead it sets the value to zero.
contract TetDelete{
mapping(string => uint) myMapping ;
function getMyMapping (string _input) returns (uint){
return myMapping[_input];
}
function setMyMapping (string _input, uint _value){
myMapping[_input] = _value;
}
function deleteMyMapping(string _input){
delete myMapping[_input];
}
}