For those of you crazy kids out there that need to travel here is your opportunity. I suspect that this page will get very big as time goes on but I wanted to just start with the two organizations I have used and seen.
Stuff You Rucksack is a super cool site. I first saw it when I was on a mission trip in Liberia, West Africa. The concept is very simple. If you are already traveling to a certain region of the world you simply look up the country on SYR. Once you find it the site will tell you about schools, NGOs, orphanages and other organizations that need simple supplies like markers, pencils, glue, etc. The concept is that you bring stuff that you can fit in your rucksack (backpack for all of us Americans)
RCPD Nepal is a international organization that places volunteers mostly for educational use. No formal experience is required to participate but the experience is amazing. I have personally used them before. I was with the first group to teach novice monks english in a 500 year old monastery in the Himalayas. They have teaching opportunities all over and were extremely helpful. I highly recommend them except for the hostels :-)