Plain Old Data types with private members?

In C++03, it's definitely not a POD. According to §9/4, "A POD-struct is an aggregate class ...", and according to §8.5.1/1:

An aggregate is an array or a class (clause 9) with no user-declared constructors (12.1), no private or protected non-static data members (clause 11), no base classes (clause 10), and no virtual functions (10.3)."

Under C++0x, at least as of N3090/3092, I believe it is a POD. These require only that all non-static members have the same access, not that the access is necessarily public. This is to fix a problem that I believe I was the first to point out -- in C++98/03, a vacuous access specifier leads to a problem:

struct x { 
    int a;
public:
    int b;
public:
   int c;
};

This fits the requirements of a POD struct -- but the standard still gives permission for the relative positions of b and c to be swapped because of the intervening access specifier. As a result, being a POD struct doesn't provide the layout guarantees that were intended to ensure compatibility with C structs (for the obvious example).

From C++11 on, the easiest by far is to ask the compiler with std::is_pod:

#include <iostream>
#include <type_traits>

struct Demo
{
     private:
       int x;
       int y;
};

int main()
{
    std::cout << std::boolalpha;
    std::cout << std::is_pod<Demo>::value << std::endl;
}

true