This works just fine:
#include <iostream>
#include <string>
int main()
{
    int count = 4;
    std::string* stringArray = new std::string[count];
    for (int i = 0; i < count; i++)
    {
        std::cin >> stringArray[i];
    }
    for (int i = 0; i < count; i++)
    {
        std::cout << "stringArray[" << i << "] = " << stringArray[i] << std::endl;
    }
    delete [] stringArray;
    return 0;
}
Though, the better solution would still be:
int main()
{
    std::vector<std::string> stringVector;
    std::cout << "Enter Strings (Ctrl-Z to finish):" << std::endl;
    std::copy(std::istream_iterator<std::string>(std::cin), std::istream_iterator<std::string>(), std::back_inserter<std::vector<std::string>>(stringVector));
    std::copy(stringVector.begin(), stringVector.end(), std::ostream_iterator<std::string>(std::cout, "\n"));
    return 0;
}