One of the better examples of this is World Vision. They are explicitly Christian; you can donate money to them specifically for the purpose of distributing Bibles and so on, and their newsletters are chock full of Bible verses. But they also do things like distribute emergency food aid in disaster areas, and support long term development in impoverished areas worldwide by building schools, roads, medical clinics, water pumps, and giving out micro loans and small business training/advice to help people start businesses. There are secular charities that do these things, too. But I would hate to see the world deprived of even one organization that gives people practical help to improve their lives, and in this case religion is what drives this charity.
I sponsor a kid through World Vision. She turned four a few days ago, lives in a village in Sri Lanka, and is pretty much the most adorable thing in the world. Today I figured out how to get her picture online, hence this post!