By definition, no river flows upstream because upstream means going in the opposite direction of the river's current. However, several rivers flow from south to north because the source is in the higher elevation in the south. Examples of south to north flowing rivers include the Nile, Lena, Shenandoah and Little Bighorn.
The Nile River in Africa, at 4,150 miles, is the world's largest river to flow south to north. One of the smallest rivers to flow north is the Saginaw, which is 20 miles and located in Michigan. Rivers flow downstream from a higher elevation to a lower elevation, unless the land is completely flat.