C++ is all about memory ownership - aka ownership semantics.
It is the responsibility of the owner of a chunk of dynamically allocated memory to release that memory. So the question really becomes who owns the memory.
In C++ ownership is documented by the type a raw pointer is wrapped inside thus in a good (IMO) C++ program it is very rare (rare, not never) to see raw pointers passed around (as raw pointers have no inferred ownership thus we can not tell who owns the memory and thus without careful reading of the documentation you can't tell who is responsible for ownership).
Conversely, it is rare to see raw pointers stored in a class each raw pointer is stored within its own smart pointer wrapper. (N.B.: If you don't own an object you should not be storing it because you can not know when it will go out of scope and be destroyed.)
So the question:
Lets keep 1 type of semantic ownership per answer so they can be voted up and down individually.
Conceptually, smart pointers are simple and a naive implementation is easy. I have seen many attempted implementations, but invariably they are broken in some way that is not obvious to casual use and examples. Thus I recommend always using well tested smart pointers from a library rather than rolling your own. std::auto_ptr or one of the Boost smart pointers seem to cover all my needs.
std::auto_ptr<T>:Single person owns the object. Transfer of ownership is allowed.
Usage: This allows you to define interfaces that show the explicit transfer of ownership.
boost::scoped_ptr<T>Single person owns the object. Transfer of ownership is NOT allowed.
Usage: Used to show explicit ownership. Object will be destroyed by destructor or when explicitly reset.
boost::shared_ptr<T> (std::tr1::shared_ptr<T>)Multiple ownership. This is a simple reference counted pointer. When the reference count reaches zero, the object is destroyed.
Usage: When an object can have multiple owers with a lifetime that can not be determined at compile time.
boost::weak_ptr<T>:Used with shared_ptr<T> in situations where a cycle of pointers may happen.
Usage: Used to stop cycles from retaining objects when only the cycle is maintaining a shared refcount.
For me, these 3 kinds cover most of my needs:
shared_ptr - reference-counted, deallocation when the counter reaches zero
weak_ptr - same as above, but it's a 'slave' for a shared_ptr, can't deallocate
auto_ptr - when the creation and deallocation happen inside the same function, or when the object has to be considered one-owner-only ever. When you assign one pointer to another, the second 'steals' the object from the first.
I have my own implementation for these, but they are also available in Boost.
I still pass objects by reference (const whenever possible), in this case the called method must assume the object is alive only during the time of call.
There's another kind of pointer that I use that I call hub_ptr. It's when you have an object that must be accessible from objects nested in it (usually as a virtual base class). This could be solved by passing a weak_ptr to them, but it doesn't have a shared_ptr to itself. As it knows these objects wouldn't live longer than him, it passes a hub_ptr to them (it's just a template wrapper to a regular pointer).