If you are deriving from a class without a virtual destructor then Public inheritance leads to a chance that users of the class can call delete on a pointer-to-base, which leads to undefined behaviour.
In such an scenario it makes sense to use private Inheritance.
Most common example of this is to derive privately from STL containers which do not have virtual destructors.
C++FAQ has an excellent example of Private Inheritance which extends to many real live scenarios.
A legitimate, long-term use for private inheritance is when you want to build a class Fred that uses code in a class Wilma, and the code from class Wilma needs to invoke member functions from your new class, Fred. In this case, Fred calls non-virtuals in Wilma, and Wilma calls (usually pure virtuals) in itself, which are overridden by Fred. This would be much harder to do with composition.
Code Example:
class Wilma {
protected:
void fredCallsWilma()
{
std::cout << "Wilma::fredCallsWilma()\n";
wilmaCallsFred();
}
virtual void wilmaCallsFred() = 0; // A pure virtual function
};
class Fred : private Wilma {
public:
void barney()
{
std::cout << "Fred::barney()\n";
Wilma::fredCallsWilma();
}
protected:
virtual void wilmaCallsFred()
{
std::cout << "Fred::wilmaCallsFred()\n";
}
};