I volunteered with Hands On in New Orleans after Hurricane Katrina. They do an amazing job, and unlike the Red Cross they do not spent millions on administrative costs but instead provide just enough to comfortably house and feed volunteers while giving their most to those in need.<p>edit: 
Just for more info: the group I was with stayed in a church that allowed us to use their spare space to set up bunks for about 100 volunteers. We ate entirely off of donation giftcards from the local Winn-Dixie supermarket. Home Depot donated most, if not all, of the tools and a truck. An Americorps team(who brought several minivans along) lead several teams of volunteers in the actual work. The entire operation had almost 0 expenses and was very well run.