C++ "virtual" keyword for functions in derived classes. Is it necessary?

The 'virtualness' of a function is propagated implicitly, however at least one compiler I use will generate a warning if the virtual keyword is not used explicitly, so you may want to use it if only to keep the compiler quiet.

From a purely stylistic point-of-view, including the virtual keyword clearly 'advertises' the fact to the user that the function is virtual. This will be important to anyone further sub-classing B without having to check A's definition. For deep class hierarchies, this becomes especially important.

They are exactly the same. There is no difference between them other than that the first approach requires more typing and is potentially clearer.

The virtual keyword is not necessary in the derived class. Here's the supporting documentation, from the C++ Draft Standard (N3337) (emphasis mine):

10.3 Virtual functions

2 If a virtual member function vf is declared in a class Base and in a class Derived, derived directly or indirectly from Base, a member function vf with the same name, parameter-type-list (8.3.5), cv-qualification, and ref-qualifier (or absence of same) as Base::vf is declared, then Derived::vf is also virtual (whether or not it is so declared) and it overrides Base::vf.

No, the virtual keyword on derived classes' virtual function overrides is not required. But it is worth mentioning a related pitfall: a failure to override a virtual function.

The failure to override occurs if you intend to override a virtual function in a derived class, but make an error in the signature so that it declares a new and different virtual function. This function may be an overload of the base class function, or it might differ in name. Whether or not you use the virtual keyword in the derived class function declaration, the compiler would not be able to tell that you intended to override a function from a base class.

This pitfall is, however, thankfully addressed by the C++11 explicit override language feature, which allows the source code to clearly specify that a member function is intended to override a base class function:

struct Base {
    virtual void some_func(float);
};

struct Derived : Base {
    virtual void some_func(int) override; // ill-formed - doesn't override a base class method
};

The compiler will issue a compile-time error and the programming error will be immediately obvious (perhaps the function in Derived should have taken a float as the argument).

Refer to WP:C++11.