I would like to find shapefile data for all of the rivers in Puerto Rico. This could be as a subset of the rivers in the United States. I already have an accurate boundary of the island.
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Here are the open data sets that match your requirements:
Seems to be the same data sets, but available via geoplatform.gov site:
I found the Puerto Rico GIS centre's pages at http://www2.pr.gov/agencias/gis/Pages/default.aspx. Sadly I don't speak enough (any) Spanish to work out if there are any data files there but I did find a WMS of the hydrography, which suggests there is likely to be a shapefile somewhere.