I think Reading is Fundamental is one of the most famous book-related charities active today. It is, factually, the largest nonprofit focusing on children's literacy in the US. RIF helps put books in the hands of children under eight and instill those children with a love of reading. This organization is one of the first things I posted about, way back in 2008. RIF provides a number of resources including activities and booklists. You can donate, volunteer, advocate, shop - there are a number of ways to help Reading is Fundamental.
RIF has a three-star rating from Charity Navigator.