You can download hydrology shapefiles from here for a number of countries around the world. Select your country of choice and Inland water as your subject. You should receive 2 types of shapefiles:
- A line shapefile depicting line features for rivers, canals and basins
- A polygon shapefile depicting area features for rivers, canals and basins
I believe there are 5 main countries the Niger River flows through (in order from source to mouth):
- Guinea
- Mali
- Niger
- Benin
- Nigeria

I find that merging the shapefiles of the same type (ie. all line shapefiles) would be very useful when performing analytics such as querying for specific rivers (ie. the Niger River).
I use QGIS 2.2 and I merge the shapefiles via Vector > Data Management Tools > Merge shapefiles to one:

I can then, for fun, do a query (Layer > Query...) for only the Niger River to see what it looks like. The attributes for the shapefiles contain the names of rivers, in this, case I used the following expressions:
"Nam" = 'Niger'
for the merged lines.
"Name" = 'Niger'
for merged areas.

Note that there are small breaks in between certain places but most line features (light blue) connect with the area features (dark blue). Below is the final result of all the rivers in the countries named above using the OpenLayers plugin as the background:
