Are there any free volunteer summer programs to go abroad with?

There are fewer and fewer free volunteer NGO experiences to be had. Students almost always have to pay an NGO or a private company to find a volunteer placement position abroad. Some NGOs (especially faith-based NGOs) require that you fundraise to meet your travel and accommodation expenses. Students can save money if they arrange their own placement directly with a third-world NGO, but this is only recommended for those who are very independent and have a high degree of risk tolerance. Students who do choose this route, however, often have more powerful and meaningful cross-cultural experiences.

If you are short on funds and want a more structured experience (with less risk), consider teaching English abroad to finance your stay and seek out volunteer experiences while living in your host country. If you want to teach abroad during the summer months, consider Chile or another South American country. Think about intensifying your cross-cultural learning by pursuing language learning, travel and professional networking while you are abroad. All of these experiences can help students maximize the “professional value” of their time abroad, and the experiences can be subsidized by teaching English.

A summer abroad usually entails periods of two months or less abroad, and while it can be a great start to building your International IQ, it should be noted that this short amount of time is usually not enough to get the experience of full cultural immersion. Students who wish to gain long-term cross-cultural skills should go abroad for four or more months. Consider working in the US for the first two months of your summer break to save some money, and then go abroad for four full months (i.e. take the fall semester off and create a gap semester abroad for yourself).

Check out Volunteer Abroad and NGOs & International Development (for registered users) for more info. 

Hope this helps.
Jean-Marc