Virtual destructors are useful when you might potentially delete an instance of a derived class through a pointer to base class:

class Base 
{
    // some virtual methods
};

class Derived : public Base
{
    ~Derived()
    {
        // Do some important cleanup
    }
};

Here, you'll notice that I didn't declare Base's destructor to be virtual. Now, let's have a look at the following snippet:

Base *b = new Derived();
// use b
delete b; // Here's the problem!

Since Base's destructor is not virtual and b is a Base* pointing to a Derived object, delete b has undefined behaviour:

[In delete b], if the static type of the object to be deleted is different from its dynamic type, the static type shall be a base class of the dynamic type of the object to be deleted and the static type shall have a virtual destructor or the behavior is undefined.

In most implementations, the call to the destructor will be resolved like any non-virtual code, meaning that the destructor of the base class will be called but not the one of the derived class, resulting in a resources leak.

To sum up, always make base classes' destructors virtual when they're meant to be manipulated polymorphically.

If you want to prevent the deletion of an instance through a base class pointer, you can make the base class destructor protected and nonvirtual; by doing so, the compiler won't let you call delete on a base class pointer.

You can learn more about virtuality and virtual base class destructor in this article from Herb Sutter.