I like
Doctors Without Borders | MSF USA,
.: Sisters Of The Road, Inc. :. (which is local and feeds the hungry and advocates for the homeless) and
Outside In :: Serving homeless youth and low-income adults in Portland Oregon, (which I've volunteered at, they provide support for homeless youth and health care for the uninsured and have a needle exchange).
They are all secular, they get money from some religious organizations, but they are not themselves religious.