Debug assertion failed. C++ vector subscript out of range

Regardless of how do you index the pushbacks your vector contains 10 elements indexed from 0 (0, 1, …, 9). So in your second loop v[j] is invalid, when j is 10.

This will fix the error:

for(int j = 9;j >= 0;--j)
{
    cout << v[j];
}

In general it’s better to think about indexes as 0 based, so I suggest you change also your first loop to this:

for(int i = 0;i < 10;++i)
{
    v.push_back(i);
}

Also, to access the elements of a container, the idiomatic approach is to use iterators (in this case: a reverse iterator):

for (vector<int>::reverse_iterator i = v.rbegin(); i != v.rend(); ++i)
{
    std::cout << *i << std::endl;
}