I've been plugging a relief organization called Operation USA. Over the years, I've donated a lot of loot to causes and then found out that only about 30% of what I gave was actually going to feed the hungry or heal the sick, and 70% was going for administrative expenses or so the head of the organization could drive a Bentley to fund-raising events. When I met the folks behind Operation USA, I was impressed with…well, with how shabby their offices were, for one thing. And I was impressed with them. I then called someone I knew who was with a government agency that monitors charities to make sure they use at least some of your donations for their attended purpose. I asked about Operation USA and my friend there said, "Oh, they're one of the best! They do so much good."
That was enough for me but I'm happy to have corroboration. Corey Klemow (thanks, Corey) found this site which checks up on charities and tells you where their money goes. The listing for Operation USA says they're everything I always believed.