I wanted a way to have error code (int) and string description (any string) be declared in one and only one single place and none of the examples above allows that.
So I declared a simple class storing both int and string and maintaining a static map for int->string conversion. I also added an "auto-cast to" int function:
class Error
{
public:
    Error( int _value, const std::string& _str )
    {
        value = _value;
        message = _str;
#ifdef _DEBUG
        ErrorMap::iterator found = GetErrorMap().find( value );
        if ( found != GetErrorMap().end() )
            assert( found->second == message );
#endif
        GetErrorMap()[value] = message;
    }
    // auto-cast Error to integer error code
    operator int() { return value; }
private:
    int value;
    std::string message;
    typedef std::map<int,std::string> ErrorMap;
    static ErrorMap& GetErrorMap()
    {
        static ErrorMap errMap;
        return errMap;
    }
public:
    static std::string GetErrorString( int value )
    {
        ErrorMap::iterator found = GetErrorMap().find( value );
        if ( found == GetErrorMap().end() )
        {
            assert( false );
            return "";
        }
        else
        {
            return found->second;
        }
    }
};
Then, you simply declare your error codes as below:
static Error ERROR_SUCCESS(                 0, "The operation succeeded" );
static Error ERROR_SYSTEM_NOT_INITIALIZED(  1, "System is not initialised yet" );
static Error ERROR_INTERNAL(                2, "Internal error" );
static Error ERROR_NOT_IMPLEMENTED(         3, "Function not implemented yet" );
Then, any function returning int can do to return 1
return ERROR_SYSTEM_NOT_INITIALIZED;
And, client programs of your library will get "System is not initialised yet" when calling
Error::GetErrorString( 1 );
or:
Error::GetErrorString( ERROR_SYSTEM_NOT_INITIALIZED );
The only limitation I see is that static Error objects are created many times if .h file declaring them is included by many .cpp (that's why I do a _DEBUG test in constructor to check consistency of the map). If you don't have thousands of error code, it should not be a problem (and there may be a workaround...)