Solution 1:

If you need to iterate over a queue then you need something more than a queue. The point of the standard container adapters is to provide a minimal interface. If you need to do iteration as well, why not just use a deque (or list) instead?

Solution 2:

While I agree with others that direct use of an iterable container is a preferred solution, I want to point out that the C++ standard guarantees enough support for a do-it-yourself solution in case you want it for whatever reason.

Namely, you can inherit from std::queue and use its protected member Container c; to access begin() and end() of the underlying container (provided that such methods exist there). Here is an example that works in VS 2010 and tested with ideone:

#include <queue>
#include <deque>
#include <iostream>

template<typename T, typename Container=std::deque<T> >
class iterable_queue : public std::queue<T,Container>
{
public:
    typedef typename Container::iterator iterator;
    typedef typename Container::const_iterator const_iterator;

    iterator begin() { return this->c.begin(); }
    iterator end() { return this->c.end(); }
    const_iterator begin() const { return this->c.begin(); }
    const_iterator end() const { return this->c.end(); }
};

int main() {
    iterable_queue<int> int_queue;
    for(int i=0; i<10; ++i)
        int_queue.push(i);
    for(auto it=int_queue.begin(); it!=int_queue.end();++it)
        std::cout << *it << "\n";
    return 0;
}

Solution 3:

you can save the original queue to a temporary queue. Then you simply do your normal pop on the temporary queue to go through the original one, for example:

queue tmp_q = original_q; //copy the original queue to the temporary queue

while (!tmp_q.empty())
{
    q_element = tmp_q.front();
    std::cout << q_element <<"\n";
    tmp_q.pop();
} 

At the end, the tmp_q will be empty but the original queue is untouched.

Solution 4:

One indirect solution can be to use std::deque instead. It supports all operations of queue and you can iterate over it just by using for(auto& x:qu). It's much more efficient than using a temporary copy of queue for iteration.