Unfortunately Christoph's solution as written only works in very limited circumstances. [EDIT: as commented below I no longer remember my reasoning for this sentence and it is likely wrong: "Note that this will only work in abstract classes, first of all."] The next difficulty is that g() only works from DIRECT subclasses of A. We can fix that, though:
private Class<?> extractClassFromType(Type t) throws ClassCastException {
    if (t instanceof Class<?>) {
        return (Class<?>)t;
    }
    return (Class<?>)((ParameterizedType)t).getRawType();
}
public Class<B> g() throws ClassCastException {
    Class<?> superClass = getClass(); // initial value
    Type superType;
    do {
        superType = superClass.getGenericSuperclass();
        superClass = extractClassFromType(superType);
    } while (! (superClass.equals(A.class)));
    Type actualArg = ((ParameterizedType)superType).getActualTypeArguments()[0];
    return (Class<B>)extractClassFromType(actualArg);
}
This will work in many situations in practice, but not ALL the time. Consider:
public class Foo<U,T extends Collection<?>> extends A<T> {}
(new Foo<String,List<Object>>() {}).g();
This will throw a ClassCastException, because the type argument here isn't a Class or a ParameterizedType at all; it's the TypeVariable T. So now you would be stuck trying to figure out what type T was supposed to stand for, and so on down the rabbit hole.
I think the only reasonable, general answer is something akin to Nicolas's initial answer -- in general, if your class needs to instantiate objects of some other class that is unknown at compile-time, users of your class need to pass that class literal (or, perhaps, a Factory) to your class explicitly and not rely solely on generics.