If you're only on a short trip, take time to visit an orphanage, hospital, etc. Those with more time can contact local NGOs, tourist offices, embassies, etc to inquire about longer term possibilities.
There are several ways to combine traveling and voluntary work:
In Europe, young people can participate in an EVS program, European Voluntary Service , which allows them to work abroad for 3 months up to a year, funded by the European union at some kind of charitable organization.
If you would like to combine traveling and working on an organic farm, the WWOOF-ing - Willing Workers on Organic Farms  - might be something for you. You can be sowing seed, making compost, gardening, planting, cutting wood, weeding, making mud-bricks, harvesting, fencing, building, packing, milking and feeding livestock any of 80 countries. A similar organization that includes opportunities beyond the scope of just organics is HelpX .
If you would like to work in an international work camp for two weeks as an alternative holiday, contact your national branch of SCI .
If you pay US income taxes, you may be able to take a charitable deduction for some or all of your trip expenses. The IRS is very strict on which organizations' trips qualify, and if you combine volunteer work with vacation, you will have to prorate the deduction on your airfare.
Various agencies of Western governments send volunteers abroad: the US Peace Corps , British VSO , Canadian CUSO  and so on. These are among the best volunteer jobs. All expenses — immunizations, travel, lodging, etc. — are normally covered and there is support — training, medical insurance, emergency evacuation if needed — and some sort of small salary. When you come back, these organizations look good on a resume. On the other hand, these positions are harder to get and usually require a heavier commitment, typically two years.
There are also various organizations that recruit volunteers. These may not cover the major expenses such as travel. Some charge a fee for placement. A few of these are:
AFECT offers volunteering opportunities to assist Burmese refugees in north Thailand 
Akha Asia has volunteer placements with Tribes and Indiginous Peoples