A frequent source of these bugs is when you have a method that accepts a reference or pointer to an object but leaves ownership unclear. Style and commenting conventions can make this less likely.
Let the case where the function takes ownership of the object be the special case. In all situations where this happens, be sure to write a comment next to the function in the header file indicating this. You should strive to make sure that in most cases the module or class which allocates an object is also responsible for deallocating it.
Using const can help a lot in some cases. If a function will not modify an object, and does not store a reference to it that persists after it returns, accept a const reference. From reading the caller's code it will be obvious that your function has not accepted ownership of the object. You could have had the same function accept a non-const pointer, and the caller may or may not have assumed that the callee accepted ownership, but with a const reference there's no question.
Do not use non-const references in argument lists. It is very unclear when reading the caller code that the callee may have kept a reference to the parameter.
I disagree with the comments recommending reference counted pointers. This usually works fine, but when you have a bug and it doesn't work, especially if your destructor does something non-trivial, such as in a multithreaded program. Definitely try to adjust your design to not need reference counting if it's not too hard.