I have the same interest as you. I would love to work for a relief organisation. I want to be a nurse. Some organisations I have heard of are: The Red Cross, Habitat for Humanity, and Doctors Without Borders.
There are also some Christian organisations like Youth For Christ, Youth With A Mission, Samaritan's Purse, and so on. For most serious missions I think you would need to have extensive training (like be a doctor/paramedic/RN, have construction/plumbing/electrical experience and training, etc.) By the way, YFC and YWAM don't require you to be a "youth" and prior experience or knowlege isn't necessary. They are Christian organsiations, though, so you would need to be a born again Christian and be willing to witness to the locals.
For example, some people I know did a mission a few years ago to El Salvador and built a new church for a congregation who lost their church in an earthquake. I think they might have built a house there also, but I can't remember.
I hope that helps. I am looking forward to hearing other people's firsthand experiences, also.