I sponsor a child through Plan Canada (Their "Because I Am a Girl" campaign). They are non for profit, have no religious or political affiliation, and have a 80:20 rule of allocation. They also give you good updates (I think twice a year) on what is going on with your sponsor child and its effects on the community.
The only downside is that they do call once in while and ask you to sponsor another child, but they are never overly pushy.
http://plancanada.ca/