Hi there,
I am not sure if my experiences would be at all what you are looking for, but thought I'd share them as well.
Also, while I appreciate all the opinions voiced on here, I do feel that volunteering can have -- and has had -- a positive impact in many places worldwide. Whether or not it does of course depends on the organization and many other factors.
In any case -- I lived in India for 1.5 years, during which time I experienced volunteering at a few different projects.
Prior to this I volunteered in Tanzania for an organization called "Volunteer Africa" -- which was a wonderful experience, but for which you actually have to *pay* money (yes, to volunteer) -- so while a great experience and I will always remember affectionately the kids and others we worked with there, it is not something I recommend to others except those learning to burn money.
A lot of *free* or *cheap* volunteer opportunities I found in India, on the other hand.
Most of these did not involve teaching.
However, if you are looking specifically for teaching, I recall.... well, it was not precisely *teaching* per se, but rather English Conversation leading volunteering, which I did in Mcleod Ganj, Dharamsala (India), which was English conversation primarily for (Tibetan exile) Buddhist monks. They accept both men and women there -- there were many females in fact. Overall these organizations have a great atmosphere, and were very wonderful places to spend some time (I do not remember all of the names -- one of the names I do remember is "Tibetan Hope Centre" (I believe) in Mcleod Ganj, Dharamsala. Wonderful place).
Dharamsala is a beautiful place which is the seat of the Dalai-Lama and his government-in-exile, and stunning mountain vistas, and clean mountain air, which is quite refreshing after being in the cities of India.... If you ever find yourself in India I would highly recommend visiting Dharamsala (McLeod Ganj) and spending some time there.
In terms of volunteering for quite *cheap*, another place I can recommend is Sadhana Forest in Tamil Nadu (South India). For about $5 USD per day (and the work you do), you are given accommodation and three (wonderful, Vegan) meals. So it is a very cheap (and outdoor) place to live. That said, the work is not generally teaching, it is re-forestation and plenty of other work (PM me for more details I will be happy to share), although there is also an adjoining Children's project there, where you can work if you commit to staying at least 4 weeks, which does not so much teach English, but rather teaches according to philosophies of "student-centred education" or "unschooling." They are always happy to have volunteers, and again, if you don't mind "roughing it" a little bit, it is great value for about $5 per day with all accommodation and meals included. Nice atmosphere too.
sadhanaforest.org/I believe they have also opened branches in Kenya and Haiti also -- though those do not I believe have the Children's projects.
Best of luck, and I hope and am sure you will find a place that is fulfilling where you can share your skills!