Bhutan is a mountainous country located between India and China. It has controlled its tourism by requiring all international tourists to visit Bhutan through a local registered tourist agency, and charging a high fee. This is done to maximize the money gained from tourism while minimizing the cultural and environmental impact.
Volunteers to Bhutan do not have to pay the daily fee and visit through a guided tour, making it an attractive option to some travelers. However, in order to volunteer in Bhutan you will need special technical skills that is lacking in the local community.
A couple of the organizations that work in Bhutan are:
Japanese International Cooperation Agency (Japan)
UN Volunteers Program
You may also try the Idealist.org website, which is a database of volunteer and job opportunities for around the world. You can narrow search results by country.
Bhutan Travel Guide