iterate vector, remove certain items as I go

The erase() method returns a new (valid) iterator that points to the next element after the deleted one. You can use this iterator to continue with the loop:

std::vector<std::string>::iterator iter;
for (iter = m_vPaths.begin(); iter != m_vPaths.end(); ) {
    if (::DeleteFile(iter->c_str()))
        iter = m_vPaths.erase(iter);
    else
        ++iter;
}

Check out std::remove_if:

#include <algorithm> // for remove_if
#include <functional> // for unary_function

struct delete_file : public std::unary_function<const std::string&, bool> 
{
    bool operator()(const std::string& strPath) const
    {
        return ::DeleteFile(strPath.c_str());
    }
}

m_vPaths.erase(std::remove_if(m_vPaths.begin(), m_vPaths.end(), delete_file()),
                m_vPaths.end());

Use a std::list to stop the invalid iterators problem, though you lose random access. (And cache performance, in general)

For the record, the way you would implement your code would be:

typedef std::vector<std::string> string_vector;
typedef std::vector<std::string>::iterator string_vector_iterator;

string_vector_iterator iter = m_vPaths.begin();
while (iter != m_vPaths.end())
{
    if(::DeleteFile(iter->c_str()))
    {
        // erase returns the new iterator
        iter = m_vPaths.erase(iter);
    }
    else
    {
        ++iter;
    }
}

But you should use std::remove_if (reinventing the wheel is bad).