You never said anything about what it is that you can do. What are your areas of expertise? Can you work in a language other than English?
Here is a web site that can help you learn more about the skills and experience desired by organizations that don't charge volunteers but require volunteers to be highly-skilled, and how you can start to gain such experience locally, wherever you are right now:
If you skills and experience that are very much needed in the developing world -- you've managed a literacy project, you've built a water filtration system using local materials, you've directed an HIV/AIDS awareness campaign with teenagers, you've helped establish a farmer's co-op, you've provided medical services, you've helped with a prisoner education program, etc. -- then you can look into SCI - Service Civil International ((http://www.sci-ivs.org/)
and Winrock International. Both are based in the USA and have short-term assignments for highly-skilled, expert volunteers. Look at their web sites to get an idea of the kinds of experts they are looking for.
Without skills that are very much needed in the developing world, you are an unskilled volunteer, and will need to pay all expenses associated with your experience: flights, in-country transportation, health insurance, accommodation, food, security, translators, training, staff to create the service opportunities and then to supervise and support you in your service, liaisons with the police and local officials, etc. The reason is that the organization wants to spend it's money hiring local people for unskilled jobs, so they can gain experience and feed their families.
There is a listing of the more-than-30 member organizations of the International Volunteers Program Association (IVPA) that is a good place to find reputable volunteer-for-a-fee programs -- programs where you don't need to have much experience in order to participate, and the placements are just for a few weeks or months:
Here's one specific org recommendation for a pay-to-volunteer program: Unite For Sight, which workes through partner eye clinics and communities to create eye disease-free communities. "While helping the community, volunteers are in a position to witness and draw their own conclusions about the failures and inequities of global health systems. It broadens their view of what works, and what role they can have to insure a health system that works for everyone..." This program was featured on CNN International. Volunteers, both skilled and unskilled, are 18 years and older, and there is no upper age limit. It is obligatory for accepted volunteers to purchase insurance coverage through Unite for Sight's recommended provider, and volunteers are responsible for all travel arrangements, visa vaccine requirements, lodging, airfare, food, and any additional expenses. http://www.uniteforsight.org/intl_volunteer/