Natural Earth provides the global river network polyline shape file as "Rivers + lake centerline".
This data is supposed to supersede the DNNET (River Drainage Network Data), part of the Digital Chart of the World, which was used by Duflo and Pande (2007) to locate rivers in India and to calculate the average river gradient in each district of India to predict the number of dams constructed. Penn State University's Library, which used to host the Digital Chart of the World, now directs data users to Natural Earth.
CIA World DataBank II offers the spatial data on navigable rivers. See this post on CIA World DataBank II.